E. Fiandrini 1 Cenni di Cosmologia Cose la cosmologia scientifica Breve storia della nostra...

E. FiandriniE. Fiandrini 11

Cenni di Cosmologia Cenni di Cosmologia

•Cos’e’ la cosmologia scientifica•Breve storia della nostra concezione dell’universo•Le osservazioni e gli sviluppi fondamentali del XX secolo•La relativita’ generale•Infinatemente piccolo e Infinitamente grande•Il modello standard dell’universo ai nostri giorni•Possibili evoluzioni del nostro modo di concepire l’universo


Cominciamo...dalla fineCominciamo...dalla fine

The Nobel Prize in Physics 2006

"for their discovery of the blackbody form and anisotropy of the cosmic

microwave background radiation"

John C. Mather

George F. Smoot


Cos’e’ la CosmologiaCos’e’ la CosmologiaCosmologia scientifica:descrizione dell’Universo nel suo insieme a partire dalle leggi fisiche fondamentali (cosi’ come le conosciamo ora!!) e da osservazioni sperimentali

Non e’ semplicemente “Cosmogonia”

Terreno nel quale si mette alla provala nostra comprensione della fisica: dove mettiamo in relazione infinitamente piccolo e infinitamente grande: non coincide con Astrofisica e Astronomia

ATTENZIONE ALLA SEPARAZIONE DA FILOSOFIAE RELIGIONE...


La nascita della La nascita della

Cosmologia Scientifica Moderna:Cosmologia Scientifica Moderna: NewtonNewton

Il seme per una nuova e razionale comprensione dell’universoesistevano gia’ prima di Newton.

A lui va il merito di aver inquadrato questa rivoluzione cognitivain un quadro (modello) teorico (matematico) di immenso potere

predittivo:

La gravitazione come forza universale:

determina l’evoluzione di qualsiasi oggetto -> quindi l’universo

sempre attrattivae additiva

in modo istantaneo!2R

MmGF


Newton’s law of gravityNewton’s law of gravity

M: mass of one object [e.g. Earth]M: mass of one object [e.g. Earth]

m: mass of the other object [e.g. apple, Moon]m: mass of the other object [e.g. apple, Moon]

r: distance between the two objectsr: distance between the two objects

F: Force with which the two objects are F: Force with which the two objects are attracting each otherattracting each other

G: gravitational constant [6.67G: gravitational constant [6.671010-11 -11 N mN m22/kg/kg22]]

2r

MmGF 2r

MmGF


Newton e i suoi contemporanei (e i posteri fino al 1920 o quasi) pensano all’ Universo come una

entita’ StaticaUn universo statico non puo’ che essere

infinitamente esteso (e omogeno, uniforme)!

Problema 1: Attenzione: in un universo infinito, se la forza e’ instantanea basta un piccolo squilibrio in un punto per creare un grande sconvolgimento....


A toy universeA toy universe

According to Newton, what is going to happen ?According to Newton, what is going to happen ?

The model Universe is going to collapse under The model Universe is going to collapse under its own gravityits own gravity

boundaryboundary

constant densityconstant density

(homogeneous)(homogeneous)


Newton’s UniverseNewton’s Universe

In order to avoid collapseIn order to avoid collapse– homogeneoushomogeneous– isotropicisotropic– infinite sizeinfinite size– no centerno center

infinite in timeinfinite in time– has always beenhas always been– will always bewill always be

perfect cosmological principleperfect cosmological principle


Questa visione apparentemente soddisfacente(universo senza confini e senza un inizio)

viene pero’ messa in crisi anche da un altro problema:“Il Paradosso di Olbers”

Perche’ di notte il cielo e’ nero?


In universo omogeneo infinito e statico da qualunque parte si guardi l’occhio incontrera’ una stella.

La compensazione e’ perfetta!: Tutto il cielo dovrebbe essere luminoso come la superficie del Sole!!

Luminosita’ in funzione della distanza D:

Numero di stelle in una “buccia” sferica adistanza D:

2DN

2

1

DL

NLLtot ~ costante

...e infinite buccie infinita luminosita'!


How to solve Olber’s paradox ?How to solve Olber’s paradox ?

The speed of light is finiteThe speed of light is finite

Universe is finiteUniverse is finite

Universe has finite ageUniverse has finite age

The distribution of stars throughout The distribution of stars throughout space is not uniformspace is not uniform

The wavelength of radiation increases The wavelength of radiation increases with time. with time.

Note:Note: for the big bang model, all thesefor the big bang model, all these conditions are satisfied conditions are satisfied


Oggi conosciamo la soluzione:-la velocita’ della luce e’ finita- Quello che vediamo sono immagini lontane che appartengono ad un Universo piu’ giovane.-Le stelle (e quindi le galassie) hanno una loro evoluzione: esiste un tempo in cui non brillavano...

t

x

noi, ora

tempo a cui la luce e’ stataemessa

segnale che si propaga con v=c

v<c

Questa stella non la possiamo ancora vedere


Einstein’s new relativityEinstein’s new relativity

Galileo:Galileo:– The The laws of mechanicslaws of mechanics are the same in all inertial are the same in all inertial

frames of referenceframes of reference– time and spacetime and space are the same in all inertial frames are the same in all inertial frames

of referenceof reference

Einstein:Einstein: – The The laws of physicslaws of physics are the same in all inertial are the same in all inertial

frames of referenceframes of reference– thethe speed of light in the vacuum speed of light in the vacuum is the same in all is the same in all

inertial frames of referenceinertial frames of reference


Minkowski’s spacetimeMinkowski’s spacetime

Time intervals, lengths, and simultaneity is Time intervals, lengths, and simultaneity is relative and depend on the relative velocity of relative and depend on the relative velocity of the observer.the observer.

velocity connects time and spacevelocity connects time and space

Let’s stop separating space and time, let’s Let’s stop separating space and time, let’s rather talk about rather talk about spacetimespacetime

spacetimespacetime is 4 dimensional, 3 spatial + 1 time is 4 dimensional, 3 spatial + 1 time dimensiondimensionbut is space and time really the same thing ?but is space and time really the same thing ?


Faster than speed of light ?Faster than speed of light ?

ct

x


A comment on superluminal speedA comment on superluminal speed

The key issue is that no information can be The key issue is that no information can be transmitted faster than the speed of light.transmitted faster than the speed of light.

This does not exclude or forbid the existence This does not exclude or forbid the existence of apparent superluminal velocities.of apparent superluminal velocities.


EnergyEnergyNewton:Newton:

– kinetic energy: kinetic energy: EEkinkin= ½ m v= ½ m v22

– v=0 v=0 E Ekinkin= 0= 0

Einstein:Einstein:

– E = E = mm00 c c22

– v=0 v=0 E= m E= m00 c c2 2 “ “rest energy”rest energy”

– EEkinkin = = ((-1) -1) mm00 c c22

Example:Example:energy required to accelerate 1kg of mass to v=0.87c energy required to accelerate 1kg of mass to v=0.87c equivalent of equivalent of 20 20 megatons of TNTmegatons of TNT

To have v=c for a particle of mass m 0, =1 particle energy must be 1 ... impossible to reach in a finite interval of time

Particles without mass can move only at v=c because they dont have inertia

1/[1-(v/c)2]1/2


geometrical intervalgeometrical interval

y

x

(x1,y1)

(x2,y2)

y

y2

x1 x2

x

s2= y2 + x2

y1


Spacetime intervalSpacetime interval

ct

x

(x1,t1)

(x2,t2)

ct

ct2

x1 x2

x

s2= (ct)2 – x2

ct1

The – sign makes the space not euclidean!


Future, past, and elsewhereFuture, past, and elsewhere

Future

Past

elsewhereelsewhere

s2>0

s2>0

s2<0

s2<0

t


Principle of causalityPrinciple of causality

Cause must always Cause must always precede the effectprecede the effect A must not influence D A must not influence D and vice versaand vice versa nothing can move nothing can movefaster than speed of lightfaster than speed of light

•A

•DSome see A happen first, Some see A happen first, some see D happen firstsome see D happen first

•C

•B

All observers agree that All observers agree that B is in the past of A and B is in the past of A and C is in the futureC is in the future

t


dt

Poiche' la luce viaggia a velocita' finita, guardare lontano significa andare indietro nella vita dell'Universo


Se l’universo non e’ statico e in particolare, se stelle e galassie si sono formate in un qualche periodo del passato e se prima di quel periodo le condizioni erano tali che non esisteva materia luminosa, allora la luce proveniente da distanze sempre piu’ grandi e’ decrescente

L’ Universo come noi lo conosciamo ha avuto un inizio

nel lontano passato?SI!


Nuovi sviluppi osservativi nei Nuovi sviluppi osservativi nei primi 20 anni del 1900primi 20 anni del 1900

Edwin Hubble contribuisce alla scoperta di nuove lontane galassie e alla misurazione della loro distanza

Mette in relazione la distanza con un fatto gia’ conosciuto:

il “red-shift” delle righe spettrali


Doppler effect (for sound)Doppler effect (for sound)

The pitch of an approaching car is higher than thatThe pitch of an approaching car is higher than that

of a car moving away.of a car moving away.


Doppler effect (for light)Doppler effect (for light)

The light of an approaching source is shifted to the blue, The light of an approaching source is shifted to the blue,

the light of a receding source is shifted to the red.the light of a receding source is shifted to the red.


velocita’ V

Effetto Doppler

c

Vemessaosservata 1

emessaosservata


Doppler effectDoppler effect

red shiftred shiftblue shiftblue shift

The light of an approaching source is shifted to the blue, The light of an approaching source is shifted to the blue,

the light of a receding source is shifted to the red.the light of a receding source is shifted to the red.


Doppler effectDoppler effect

1emessa

osservataz

c

Vemessaosservata 1

c

Vz

Si misura z e si ottiene v

Se v<<c

Red-shift e velocita' sono

la stessa cosa

Definizione di “red shift”:


Legge di Hubble: lo spostamento verso il rosso dipende dalla

distanza

dz


The redshift-distance relationThe redshift-distance relation


Key resultsKey resultsMost galaxies are moving away from usMost galaxies are moving away from us

The recession speed v is larger for more The recession speed v is larger for more distant galaxies. The relation between recess distant galaxies. The relation between recess velocity velocity vv and distance and distance dd fulfills a linear relation: fulfills a linear relation:

v = Hv = H0 0 d d

Hubble’s measurement of the constant Hubble’s measurement of the constant HH00::

HH00 = 500 km/s/Mpc = 500 km/s/Mpc

today’s best fit value of the constant:today’s best fit value of the constant: HH00 = 72 = 72 §§ 8 km/s/Mpc 8 km/s/Mpc


Tutto sembra allontanarsi (IN MEDIA) da noi

Siamo per caso in un punto speciale dell’Universo?

Crediamo di no: estensione del principio

Copernicano

al “Principio Cosmologico”

Come si puo’ quindi spiegare l’espansione che osserviamo?

ogni punto dell’universo e’ ugualea un altro e non esiste un centro


Analogia con una superficie BiDimensionale: macchie sulla superficie di un palloncino che

si gonfia

Ogni macchia vede le altre allontanarsi: non esiste nessun centro!

Ma e’ un vero movimento fisico? La risposta era gia’ nell’aria

attorno al 1920 grazie ad una rivoluzione di tipo teorico...


Expanding SpaceExpanding Space

Analogy:

A loaf of raisin bread where the dough is rising and expanding, taking the raisins with it.


La velocita’ con cui si espande R (velocita’ di recessione)

puo’ anche essere maggiore di c!

La limitazione a c vale solo percorpi materiali e raggi luminosi

Importantissimo:!!!


Nuovi sviluppi teorici nei primi 20 Nuovi sviluppi teorici nei primi 20 anni del 1900anni del 1900

Dalla Relativita’ Ristretta alla

Relativita’ Generale: (tutti i riferimenti in

cadutalibera sono equivalenti)

Presupposti matematici: “La geometria differenziale” le geometrie “non euclidee”(Gauss, Riemann, Lobacevsky, Ricci, Levi-Civita,...)

A. Einstein


Mass curves spaceMass curves space


General relativityGeneral relativity

Mass tells space how to curveMass tells space how to curve

Space tells mass how to moveSpace tells mass how to move


Some effects predicted by the Some effects predicted by the theory of general relativitytheory of general relativity

gravity bends lightgravity bends light

gravitational redshiftgravitational redshift

gravitational time dilationgravitational time dilation

gravitational length contractiongravitational length contraction


Least action principleLeast action principle

light travels on a path that minimizes the light travels on a path that minimizes the distance between two pointsdistance between two points for flat space: straight line for flat space: straight line

a path that minimizes the distance a path that minimizes the distance between two points is called a between two points is called a geodesicgeodesic

Examples for geodesicsExamples for geodesics– plane: straight lineplane: straight line– sphere: great circlesphere: great circle


What is the shortest way to What is the shortest way to Europe?Europe?


Flat spaceFlat space

++ = 180º


Curved spaceCurved space

++ 180º


Flat spaceFlat space

circumference = 2 radius


Curved spaceCurved space

circumference 2 radius


The metric equationThe metric equation

Distance between two points (flat euclidean Distance between two points (flat euclidean space)space)

Distance between two points (curved space)Distance between two points (curved space)

f, g, h: f, g, h: metric coefficientsmetric coefficients

222 yxs 222 yxs

222 2 yhyxgxfs 222 2 yhyxgxfs


Example: distance between two Example: distance between two points at the surface of the Earthpoints at the surface of the Earth

Coordinate differences: Coordinate differences: , ,

naïve, but false:naïve, but false:

correct:correct:

metric coefficients: metric coefficients: f=Rf=R22, h= R, h= R22 coscos22

222 s 222 s

222222 cosRRs 222222 cosRRs


SpacetimeSpacetime

Fourth coordinate: Fourth coordinate: ctct

time coordinate has different sign than time coordinate has different sign than spatial coordinatesspatial coordinates

spacetime distance:spacetime distance:

, , , , :: metric coefficientsmetric coefficients

2222 xxtctcs 2222 xxtctcs


Why does space curvature result in Why does space curvature result in attraction ?attraction ?

In uno spazio curvo, due particelle si muovono lungo le

geodetiche tra due punti

La curvatura dello spazio porta le geodetiche a ridurre la loro distanza quando si muovono

NELLO spazio curvo: un osservatore NELLO spazio

vede le particelle attrarsi

Non esistono "forze", il moto e' determinato dalla curvatura

dello spazio: le particelle seguono la linea piu' breve fra

due punti


The entire Universe in one lineThe entire Universe in one line

T

c

GG

4

8

Tc

GG

4

8

Geometry of Geometry of

spacetimespacetime

(Einstein tensor)(Einstein tensor)

Distribution ofDistribution of

mass and energymass and energy

in the universein the universe

(stress-energy tensor)(stress-energy tensor)


The entire Universe in one lineThe entire Universe in one line

The solutions of Einstein's equations provide the metric of the space-time and the motion of the particles in the space-

time a in self-consistent way

The space and time are part of the solution of the equations, not the simply the background where the events occur


Why is general relativity (GR) Why is general relativity (GR) difficult ?difficult ?

conceptually difficult (relativity of space conceptually difficult (relativity of space and time, curvature of spacetime)and time, curvature of spacetime)

set of 10 coupled partial differential set of 10 coupled partial differential equations equations

non linear (solutions do not superpose)non linear (solutions do not superpose)

space and time are part of the solutionspace and time are part of the solution

exact solution known only for a very exact solution known only for a very few simple casesfew simple cases


First test: bending of lightFirst test: bending of light

Star light should be bend as it passes Star light should be bend as it passes through the gravitational field of the through the gravitational field of the Sun, i.e., it should be possible to see a Sun, i.e., it should be possible to see a star behind the Sunstar behind the Sun


First test: bending of lightFirst test: bending of light

Star light should be bend as it passes Star light should be bend as it passes through the gravitational field of the Sun, through the gravitational field of the Sun, i.e., it should be possible to see a star i.e., it should be possible to see a star behind the Sunbehind the Sun

General relativity predicts an angle of General relativity predicts an angle of 1.75”, twice as big as that predicted by 1.75”, twice as big as that predicted by Newtonian gravityNewtonian gravity

measured by Arthur Eddington in 1919. measured by Arthur Eddington in 1919. Key event for Einstein’s elevation to a Key event for Einstein’s elevation to a celebrity.celebrity.


Test 2: Perihelion shift of MercuryTest 2: Perihelion shift of Mercury

Planets do not move on perfect ellipses, Planets do not move on perfect ellipses, but ellipses are precessing. This effect but ellipses are precessing. This effect is due to the gravitational force exerted is due to the gravitational force exerted by the other planetsby the other planets


Test 2: Perihelion shift of MercuryTest 2: Perihelion shift of Mercury

Planets do not move on perfect ellipses, Planets do not move on perfect ellipses, but ellipses are precessing. This effects but ellipses are precessing. This effects is caused by the perturbing effect of the is caused by the perturbing effect of the other planets gravitational field.other planets gravitational field.

Mercury’s precession amounts to 5600” Mercury’s precession amounts to 5600” per century, but only 5557” can be per century, but only 5557” can be explained by Newtonian gravity, leaves a explained by Newtonian gravity, leaves a discrepancy of 43” per century.discrepancy of 43” per century.

General relativity predicts exactly this General relativity predicts exactly this additional precessionadditional precession


The expanding The expanding universe: How is it universe: How is it

curved?curved?


Let’s apply Einstein’s equation Let’s apply Einstein’s equation to the Universeto the Universe

What is the solution of Einstein’s equation What is the solution of Einstein’s equation for a homogeneous, isotropic mass for a homogeneous, isotropic mass distribution, ie the Universe?distribution, ie the Universe?– As in Newtonian dynamics, gravity is always As in Newtonian dynamics, gravity is always

attractiveattractive– a homogeneous, isotropic and initially static a homogeneous, isotropic and initially static

universe is going to collapse under its own universe is going to collapse under its own gravitygravity

– Alternative: expanding universe (Friedmann)Alternative: expanding universe (Friedmann)


Einstein’s proposal: cosmological Einstein’s proposal: cosmological constant constant

There is a repulsive force in the universeThere is a repulsive force in the universe vacuum exerts a pressurevacuum exerts a pressure empty space is curved rather than flatempty space is curved rather than flat

The repulsive force compensates the attractive The repulsive force compensates the attractive gravity gravity static universe is possible static universe is possible

but:but: such a universe turns out to be unstable: one such a universe turns out to be unstable: one can set up a static universe, but it simply does not can set up a static universe, but it simply does not remain staticremain static it must expand or shrink it must expand or shrink

Einstein: “greatest blunder of his life”, Einstein: “greatest blunder of his life”, butbut is it is it really … ? really … ?


La costante cosmologicaLa costante cosmologica

Essa dava luogo a un effetto Essa dava luogo a un effetto antigravitazionale (gravità repulsiva)antigravitazionale (gravità repulsiva)

Riusciva ad arrestare il collasso Riusciva ad arrestare il collasso dell’Universodell’Universo

Ciò rendeva la visione di Einstein Ciò rendeva la visione di Einstein compatibile con l’idea generale di un compatibile con l’idea generale di un Universo statico ed eternoUniverso statico ed eterno


R.G.: l’equazione di R.G.: l’equazione di EinsteinEinstein

(sistema di 10 eq.)(sistema di 10 eq.)

(Metro, Orologi) “=“ (Energia, Materia)

TGRgR 82

1

Prima formulazione...

gTGRgR 82

1aggiunta di Einstein in seconda battuta...

costantedi Newton

“CostanteCosmologica”

Energiadel

Vuoto(????)


The great synthesis (1930)The great synthesis (1930)

Meeting by Einstein, Hubble and LemaîtreMeeting by Einstein, Hubble and Lemaître– Einstein: theory of general relativityEinstein: theory of general relativity– Friedmann and Lemaître: expanding universe Friedmann and Lemaître: expanding universe

as a solution to Einstein’s equationas a solution to Einstein’s equation– Hubble: observational evidence that the Hubble: observational evidence that the

universe is indeed expandinguniverse is indeed expanding

Consequence:Consequence:– Universe started from a pointUniverse started from a point

The Big Bang Model The Big Bang Model


The Necessity of a Big BangThe Necessity of a Big Bang

If galaxies are moving away from each other with a speed proportional to distance, there must have been a beginning, when everything was concentrated in one single point:

The Big Bang!

?


A metric of an expanding UniverseA metric of an expanding Universe

Recall: flat spaceRecall: flat space

better: using spherical coordinates (better: using spherical coordinates (r,r,,,))

22222 zyxtcs 22222 zyxtcs

22222222 sin rrrtcs 22222222 sin rrrtcs



But, this was for a static space. How does But, this was for a static space. How does this expression change if we consider an this expression change if we consider an expanding space ?expanding space ?

R(t)R(t) is the so-called is the so-called scale factorscale factor

222222222 sin)( rrrtRtcs 222222222 sin)( rrrtRtcs


Griglia dicoordinate

“comoventi”: r,, la cui scala,

cioe' unita' di misura, e' R(t)

in queste coordinatele distanze rimangono

uguali durantel’espansione

Torniamo all’analogia della superficie sferica

Ci servono 3 coordinate per lo spazio:

1 raggio e 2 angoli (come la latitudine e la longitudine)

222222222 sin)( rrrtRtcs 222222222 sin)( rrrtRtcs


Non sono gli oggetti che si muovono, ma e’ il “metro”(la scala delle distanze) che si modifica...

E non e’ solo un effetto virtuale!!!

La “dinamica” dello spazio e del tempo (cioe’ la loro evoluzione nel tempo) dipende dalla materia

e dall’energia! L’ ESPANSIONE DELLO SPAZIO TEMPOE’ PREVISTA ~AUTOMATICAMENTE SECONDO LA R.G.!!!


Example: static universeExample: static universe

R(t)

t


Example: expanding at a Example: expanding at a constant rateconstant rate

R(t)

t


Example: expansion is Example: expansion is slowing downslowing down

R(t)

t


Example: expansion is Example: expansion is acceleratingaccelerating

R(t)

t


Example: collapsingExample: collapsing

R(t)

t


How old is the universe?How old is the universe?

A galaxy at distance A galaxy at distance dd recedes at velocity recedes at velocity v=Hv=H0 0 d d..

When was the position of this galaxy When was the position of this galaxy identical to that of our galaxy? Answer: identical to that of our galaxy? Answer:

0

1

Hv

dtHubble

0

1

Hv

dtHubble

ttHubbleHubble: Hubble time. For : Hubble time. For HH00 = 72 km/s/Mpc: = 72 km/s/Mpc:

ttHubbleHubble '' 13.5 Gyr 13.5 Gyr


How big is the universe?How big is the universe?We can’t tell. We can only see (and are We can’t tell. We can only see (and are affected by) that part of the universe that is affected by) that part of the universe that is closer than the distance that light can travel closer than the distance that light can travel in a time corresponding to the age of the in a time corresponding to the age of the UniverseUniverse

But we can estimate, how big the observable But we can estimate, how big the observable universe is:universe is:

0H

cctd HubbleHubble

0H

cctd HubbleHubble

ddHubbleHubble: Hubble radius. For : Hubble radius. For HH00 = 72 km/s/Mpc: = 72 km/s/Mpc:

ddHubbleHubble = 4.2 Gpc= 4.2 Gpc



But, so far, we only considered a flat But, so far, we only considered a flat space. What, if there is curvature ?space. What, if there is curvature ?

k k is the curvature constantis the curvature constant– k=0k=0: flat space: flat space– k>0k>0: spherical geometry: spherical geometry– k<0k<0: hyperbolic geometry: hyperbolic geometry

222222

2222 sin

1)( rr

kr

rtRtcs

222222

2222 sin

1)( rr

kr

rtRtcs


A metric of an expanding A metric of an expanding UniverseUniverse

But, so far, we only considered a flat But, so far, we only considered a flat space. What, if there is curvature ?space. What, if there is curvature ?


k>0k>0 k<0k<0k=0k=0


La “metrica” dello spazio-tempoLa “metrica” dello spazio-temponella relativita’ generalenella relativita’ generale

Sulla base dell’ipotesi di uniformita’ arriviamo a direche viviamo in uno spazio tridimensionale curvo

“ortogonale” ad una dimensione di tipo temporale

fattore di scalacoordinate sferiche “comoventi”

dipende dal tempo:R = R(t) secondo

la densita’ e la speciedell’ energia/materia

)(2 kS

)(sin 2

)(sinh 2

2


Ancora l’analogia BiDimensionale (attenzione!!!...)

Adesso possiamo capire meglio la legge di Hubble: la lunghezza d'onda della luce si sposta verso il

rosso perche' lo spazio-tempo vuoto si espande, ie cambia il fattore di scala R(t)


Cosmological redshiftCosmological redshift

While a photon travels from a distance While a photon travels from a distance source to an observer on Earth, the Universe source to an observer on Earth, the Universe expands in size from expands in size from RRthenthen to to RRnownow..

Not only the Universe itself expands, but also Not only the Universe itself expands, but also the wavelength of the photon the wavelength of the photon ..

emittedthen

nowreceived R

R emittedthen

nowreceived R

R


Cosmological redshiftCosmological redshift

General definition of redshift:General definition of redshift:

for cosmological redshift: for cosmological redshift:

emitted

emittedreceivedz

emitted

emittedreceivedz

then

now

emitted

received

R

Rz

1then

now

emitted

received

R

Rz

1


Cosmological redshiftCosmological redshiftExamples:Examples:– z=1 z=1 RRthenthen//RRnownow = 0.5 = 0.5

at at z=1z=1, the universe had , the universe had 50% of its present day size50% of its present day size

emitted emitted blue lightblue light (400 nm) is shifted all the way through (400 nm) is shifted all the way through the optical spectrum and is received as the optical spectrum and is received as red lightred light (800 nm) (800 nm)

– z=4 z=4 RRthenthen//RRnownow = 0.2 = 0.2

at at z=4z=4, the universe had , the universe had 20% of its present day size20% of its present day size

emitted emitted blue lightblue light (400 nm) is shifted deep into the (400 nm) is shifted deep into the infraredinfrared and is received at 2000 nmand is received at 2000 nm

– most distant astrophysical object discovered so far: most distant astrophysical object discovered so far: z=5.8z=5.8


La velocita’ con cui si espande R (velocita’ di recessione)

puo’ anche essere maggiore di c!

La limitazione a c vale solo percorpi materiali e raggi luminosi

Importantissimo:!!!


La “Legge di Hubble”La “Legge di Hubble”fattore di espansione:

Hdzc

)2001(872 11 misuraMpcskmH

v=dR/dt v=H£R(t)

Red-shift misurato: z=(r-e)/e=r /e-1

Effetto Doppler:r = e(1+v/c)


Can we calculate R(t)?Can we calculate R(t)?

We have to solve the Einstein equations but it is possible to make

analogies with a classical gravitation at the cost of loosing the real meaning of

the parameters in the equations


Come varia il fattore di Come varia il fattore di scala (R) nel tempo?scala (R) nel tempo?

Inserendo la metrica di RW nelle equazioni di Einstatin nell'ipotesi dell’isotropia e omogeneita’ dell’Universo

vale l’equazione di Friedman

densita’ di materia/energia

coefficiente di curvatura


Friedman EquationFriedman Equation

Birkhoff’s TheorumBirkhoff’s Theorum which states that the which states that the gravitational field gravitational field within a spherical hole within a spherical hole embedded within an embedded within an otherwise infinite otherwise infinite medium is zero medium is zero



Thus in a homogenous Universe we can ignore the matter outside a small sphere

m

r|| r

MmGV mGr 2

3

4Grav.

Pot.

Kin.Energy.

2

2

1rmT

Conservation of Energy const TVU

Mass in sphere

mGrrmU 22

3

4

2

1 2

3

3

4rM 1



mGrrmU 22

3

4

2

1 2 6 xr )()( tat

mxGaxamU 2222

3

82

I don’t change with time

mGxxa

am

a

U 222

2 3

82

xr )()( tat

222

22

3

8

a

UmGxx

a

am

/a2

rearrange

22

22

3

8

amx

UG

a

a

const, -kc2

Friedman Equation

2

22

3

8

a

kcG

a

a

3

a≡R


Nearly-Newtonian CosmologyNearly-Newtonian Cosmology


Fluid EquationFluid Equation

Acceleration EquationAcceleration Equation

L'universo su scala cosmologica puo' essere considerato un gas perfetto


Fluid / Conservation EquationFluid / Conservation Equation

TdSPdVdE 1st Law of Thermodynamics

Reverseable0dS

Einstein’s 2mcE 233

3

4cxa

0

t

VP

t

E4

233232

3

44 cxacxaa

t

E

5

a≡R


Fluid EquationFluid Equation

33

3

4xaV

03 2

232

c

aaP

aaa

6

Fluid Equation

TdSPdVdE 1st Law ofThermodynamics

Reverseable0dS

Einstein’s 2mcE 233

3

4cxa

233232

3

44 cxacxaa

t

E

0

t

VP

t

E4

5

324 xaat

V

6

465 + into

234 cx

032

c

P

a

a *3/a3 Fluid

Equation7

a≡R


Acceleration / Differential Friedman Acceleration / Differential Friedman EquationEquation

Friedman Equation

2

22

3

8

a

kcG

a

a

3t

2

2

2a

aaa

a

a 3

2

23

8

a

akcG

032

c

P

a

a 7

FluidEquation

2

2

22

2

4a

kc

c

PG

a

aaa

2

2

2

2

4a

kc

c

PG

a

a

a

a

Gc

PG

a

a

3

84

2

23

3

4

c

PG

a

a

AccelerationEquation

8

a≡R


We derived the acceleration equation from We derived the acceleration equation from the Friedman and fluid equationsthe Friedman and fluid equations

The acceleration equation has no new The acceleration equation has no new physicsphysics

Thus only 2 of those 3 are independentThus only 2 of those 3 are independent

The acceleration equation is interesting as The acceleration equation is interesting as it is independent of kit is independent of k

23

3

4

c

PG

a

a

Acceleration / Differential Acceleration / Differential Friedman EquationFriedman Equation

a≡R


Equation of StateEquation of State

Equation of state relates P and Equation of state relates P and Some simple equations of state we can Some simple equations of state we can considerconsider

““Matter”, “dust”, “galaxies”Matter”, “dust”, “galaxies”

RadiationRadiation

““Cosmological Constant”Cosmological Constant”

0P 1

3

2cP

2

2cP 3


Friedmann Equations for ExpansionFriedmann Equations for Expansion

a = a = scale factorscale factor

((aa00 / / aa) is proportional to (1+) is proportional to (1+zz) = ) = obsobs / / emem

kk = 0 for our flat Universe ( = 0 for our flat Universe (kk = -1 is open, = -1 is open, kk = +1 is closed) = +1 is closed)

= = energyenergy (mc (mc22 for matter) density, for matter) density, pp = pressure (can be < 0) = pressure (can be < 0)

Both pressure and energy density are gravitationally active in GRBoth pressure and energy density are gravitationally active in GR

a≡R


Newton analogyNewton analogy

Hubble RadiusHubble Radius

distant galaxydistant galaxy

FFoutsideoutside= 0= 0

A distant galaxy is subjected only to gravitational force inside the distance from center. The mass outside does not coontribute


Newton analogyNewton analogy

2R

mMGF galinside

inside 2R

mMGF galinside

inside

The galaxy is subjected to

gravitational force of the mass inside

the radius


What is the future of that galaxy ?What is the future of that galaxy ?

Critical velocity: escape speedCritical velocity: escape speed

v<vv<vescesc: galaxy eventually stops and falls : galaxy eventually stops and falls

backback

v>vv>vescesc: galaxy will move away forever: galaxy will move away forever

R

MGv insideesc

2

R

MGv insideesc

2


Let’s rewrite that a bit ...Let’s rewrite that a bit ...

<0<0 v<vv<vescesc: galaxy eventually stops : galaxy eventually stops

and falls backand falls back

>0>0 v>vv>vescesc: galaxy will move away : galaxy will move away

foreverforever

222

R

MGv inside

222

R

MGv inside


Homogeneous sphere of density Homogeneous sphere of density ::

so for the velocity:so for the velocity:

but what is but what is ? ?

222

R

MGv inside

222

R

MGv inside

2

3

8 22 RG

v 2

3

8 22 RG

v

Let’s rewrite that a bit ...Let’s rewrite that a bit ...

3

3

4RM inside 3

3

4RM inside

The energy of "free" galaxy, that is the energy of the galaxy at 1 from mass distribution


Friedmann equationFriedmann equation

same same kk as in the Robertson-Walker metric as in the Robertson-Walker metric

222

3

8kcR

Gv 222

3

8kcR

Gv

Let’s switch to general relativityLet’s switch to general relativity

222222

2222 sin

1)( rr

kr

rtRtcs

222222

2222 sin

1)( rr

kr

rtRtcs


Friedmann equationFriedmann equation

k k is the curvature constantis the curvature constant– k=0k=0: flat space, forever expanding: flat space, forever expanding– k>0k>0: spherical geometry, eventually : spherical geometry, eventually

recollapsingrecollapsing– k<0k<0: hyperbolic geometry, forever expanding: hyperbolic geometry, forever expanding

222

3

8kcR

Gv 222

3

8kcR

Gv

Let’s switch to general relativityLet’s switch to general relativity


Il nostro universo continuera’ ad espandersi?...oppure si fermera’? o collassera’ su se stesso?

Densita’critica

Le osservazioni attuali sembrano indicareche ~ 1: implicherebbe k ~ 0...

L’equazione di Friedman si puo’ anche scrivere cosi’:

(ci torniamo dopo...)


222

3

8kcR

Gv 222

3

8kcR

Gv

2

2

2

2

3

8

R

kcG

R

v

2

2

2

2

3

8

R

kcG

R

v

Can we predict the fate of the Can we predict the fate of the Universe ?Universe ?

Friedmann equation:Friedmann equation:

2

2

2

220 3

8

R

kcG

R

vH

2

2

2

220 3

8

R

kcG

R

vH

k=0k=0::

G

Hcrit

8

3 20G

Hcrit

8

3 20


If the density If the density of the Universe of the Universe ==critcrit:: flat space, forever expandingflat space, forever expanding

>>critcrit:: spherical geometry, recollapsingspherical geometry, recollapsing

< < critcrit:: hyperbolic geometry, forever hyperbolic geometry, forever

expandingexpanding

so what is the density of the universe?so what is the density of the universe?– We don’t know preciselyWe don’t know precisely >>critcrit very unlikelyvery unlikely

Can we predict the fate of Universe ?Can we predict the fate of Universe ?


k>0k>0 k<0k<0k=0k=0


Spazio a curvatura positiva (esempio bidimensionale!!)

Su una superficiecurva la somma degliangoli di un triangolo non e’ 180 gradiper K>0 la somma e’ >180per K<0 la somma e’ <180

Pero’ su una porzione molto piccola e’ difficile capirlo:da’ l’illusione che k=0

procedendo lungouna stessa direzione...

...si ritorna al punto di partenza

Definizione di spazio “chiuso”


How big is How big is critcrit ? ?

critcrit == 881010-30-30 g/cmg/cm33 1 atom per 200 liter 1 atom per 200 liter

density parameterdensity parameter 00

00 =1 =1:: flat space, forever expanding (open)flat space, forever expanding (open)

00 >1 >1:: spherical geometry, recollapsing spherical geometry, recollapsing

(closed)(closed) 00 <1 <1:: hyperbolic geometry, forever expandinghyperbolic geometry, forever expanding

G

H

crit

8

3 20

0 G

H

crit

8

3 20

0


How can we measure How can we measure 00 ? ?

Count all the mass we can “see”Count all the mass we can “see”– tricky, some of the mass may be hidden …tricky, some of the mass may be hidden …

Measure the rate at which the expansion Measure the rate at which the expansion of the universe is slowing downof the universe is slowing down– a more massive universe will slow down fastera more massive universe will slow down faster

Measure the geometry of the universeMeasure the geometry of the universe– is it spherical, hyperbolic or flat ?is it spherical, hyperbolic or flat ?


The Universe does not expand at The Universe does not expand at constant speedconstant speed acceleration acceleration

Acceleration according to Newton:Acceleration according to Newton:

acceleration parameteracceleration parameter

RG

R

MGa

3

42

R

G

R

MGa

3

42

20

20

v

aRq

20

20

v

aRq


So what’s the meaning of So what’s the meaning of qq00 ? ?

deceleration parameter deceleration parameter qq00

– qq00>0.5:>0.5: deceleration is so strong that eventually deceleration is so strong that eventually

the universe stops the universe stops expanding and starts collapsingexpanding and starts collapsing

– 0<0<qq00<0.5:<0.5: deceleration is too weak to stop deceleration is too weak to stop

expansionexpansion

– qq00<0<0: universe is accelerating the expansion: universe is accelerating the expansion

What’s the difference between What’s the difference between qq00, , 00 and and kk ??

– kk:: curvature of the universecurvature of the universe 00:: mass content of the universemass content of the universe

– qq00:: kinematics of the universe kinematics of the universe


So let’s measure So let’s measure qq0 0 !!

How do we do that?How do we do that?– Measure the rate of expansion at different Measure the rate of expansion at different

times, i.e. measure and compare the times, i.e. measure and compare the expansion based on nearby galaxies and expansion based on nearby galaxies and based on high redshift galaxiesbased on high redshift galaxies

Gravity is slowing down expansion Gravity is slowing down expansion expansion rate should be higher at high expansion rate should be higher at high redshift. redshift.


So let’s measure So let’s measure qq0 0 !!

qq00 = 0 = 0qq00 = 0.5 = 0.5

more distantmore distant

fain

ter

fain

ter

Data indicates:Data indicates:

qq00 < 0 < 0

Expansion Expansion

is acceleratingis accelerating


Science discovery of the year 1998Science discovery of the year 1998

The expansion of the universe is The expansion of the universe is accelerating !!!accelerating !!!

But gravity is always attractive, so it only But gravity is always attractive, so it only can deceleratecan decelerate

Revival of the cosmological constant Revival of the cosmological constant to to get a "repulsive" gravity for acceleration!get a "repulsive" gravity for acceleration!


k k is the curvature constantis the curvature constant– k=0k=0: flat space, flat universe: flat space, flat universe– k>0k>0: spherical geometry, closed universe: spherical geometry, closed universe– k<0k<0: hyperbolic geometry, open universe: hyperbolic geometry, open universe

222

3

8kcR

Gv 222

3

8kcR

Gv

Friedmann’s equation for Friedmann’s equation for >0 >0

33

8 2222 R

kcRG

v

33

8 2222 R

kcRG

v


but for sufficiently large but for sufficiently large a spherically curved a spherically curved universe may expand foreveruniverse may expand forever


Deceleration parameter Deceleration parameter qq for for >0 >0

Acceleration according to Newton:Acceleration according to Newton:

deceleration parameterdeceleration parameter

RG

a3

4 R

Ga

3

4

20

20

v

aRq

20

20

v

aRq

with with

RRG

a33

4

RR

Ga

33

4

2

020 v

aRq

20

20 v

aRq

203H

2

03H

If there is a cosmological constant, then it contributes to the energy/matter

content of the universe


Is the fate of the Universe well Is the fate of the Universe well determined ?determined ?

deceleration:deceleration:– ½½00 – – > 0> 0: decelerating: decelerating

– ½½00 – – < 0< 0: accelerating: accelerating

curvaturecurvature 00 + + = 1= 1: flat: flat

00 + + < 1< 1: hyperbolic: hyperbolic

00 + + > 1> 1: spherical: spherical

two equations for two variables two equations for two variables well posed well posed problemproblem

The total content of the energy/matter in the Universe is tot=o +


k=+1

=0

>0

The fate of the Universe for The fate of the Universe for >0 >0


Cosmology: the quest for 3 numbersCosmology: the quest for 3 numbersThe Hubble constant The Hubble constant HH00

how fast is the universe expandinghow fast is the universe expanding

The density parameter The density parameter 00

how much mass is in the universehow much mass is in the universe

The cosmological constant The cosmological constant the vacuum energy of the universethe vacuum energy of the universe

• current observational situation:current observational situation:

• HH00 = 72 = 72 §§ 8 km/s/Mpc 8 km/s/Mpc

00 = 0.3 = 0.3 §§ 0.04 0.04;; = 0.7 = 0.7 §§ 0.06 0.06 flat flat

spacespace


The big-bang model:The big-bang model:The life of a UniverseThe life of a Universe


How old is the Universe?How old is the Universe?

A galaxy at distance A galaxy at distance dd recedes at velocity recedes at velocity v=Hv=H0 0 d d..

When was the position of this galaxy When was the position of this galaxy identical to that of our galaxy? Answer: identical to that of our galaxy? Answer:

0

1

Hv

dtHubble

0

1

Hv

dtHubble

ttHubbleHubble: Hubble time. For : Hubble time. For HH00 = 65 = 65

km/s/Mpc: km/s/Mpc: ttHubbleHubble = 15 Gyr= 15 Gyr


The age of the Universe revisitedThe age of the Universe revisitedSo far, we have assumed that the So far, we have assumed that the expansion velocity is not changing (expansion velocity is not changing (qq00=0=0, ,

empty universe)empty universe)How does this How does this estimate change, estimate change, if the expansion if the expansion decelerates, i.e. decelerates, i.e. qq00>0 >0 ??

An An 00>0>0, , =0=0 universe is younger than 15 Gyr universe is younger than 15 Gyr

now


now

So far, we only have considered So far, we only have considered decelerating universesdecelerating universes

How does this How does this estimate change, estimate change, if the expansion if the expansion accelerates, i.e. accelerates, i.e. qq00<0 <0 ??

The age of the Universe revisitedThe age of the Universe revisited

An An >0>0 universe can be older than 15 Gyr universe can be older than 15 Gyr


00=0=0, , =0=0: : ttHubbleHubble ==1/1/HH00 = 15 Gyr = 15 Gyr

00=1=1, , =0=0: : ttHubbleHubble ==2/(32/(3HH00))= 10 Gyr= 10 Gyr

open universes with open universes with 0<0<00<1<1, , =0 =0 are are

between 10 and 15 Gyr oldbetween 10 and 15 Gyr old

closed universes with closed universes with 00>1>1, , =0 =0 are less are less

than 10 Gyr oldthan 10 Gyr old

>0 >0 increases, increases, <0 <0 decreases the age of decreases the age of the universethe universe

00=0.3=0.3, , =0.7=0.7: : ttHubbleHubble ==0.96/0.96/HH00 = 14.5 Gyr = 14.5 Gyr

The age of the Universe revisitedThe age of the Universe revisited


not directlynot directly

but we can constrain the age of the but we can constrain the age of the Universe. It must not be younger than the Universe. It must not be younger than the oldest star in the Universe.oldest star in the Universe.

How do we measure the age of stars?How do we measure the age of stars?– radioactive datingradioactive dating– stellar evolution modelsstellar evolution models

Result: age of the oldest star ~12-14 GyrResult: age of the oldest star ~12-14 Gyr

00>~1 strongly disfavored>~1 strongly disfavored

Can we measure the age of the Can we measure the age of the Universe ?Universe ?


The life of a universe – key factsThe life of a universe – key factsUnless Unless is sufficiently large (which is is sufficiently large (which is inconsistent with observations) all cosmological inconsistent with observations) all cosmological models start with a big bang.models start with a big bang.

An universe doesn’t change its geometry. A flat An universe doesn’t change its geometry. A flat universe has always been and will always be universe has always been and will always be flat, a spherical universe is always spherical and flat, a spherical universe is always spherical and so on. so on.

Two basic solutions:Two basic solutions:– eventual collapse for largeeventual collapse for large 00 or negativeor negative

– eternal expansion otherwiseeternal expansion otherwise


Unless Unless is sufficiently large (which is is sufficiently large (which is inconsistent with observations) all inconsistent with observations) all

cosmological models start with a big bang: the cosmological models start with a big bang: the density of the Universe, treated as a perfect density of the Universe, treated as a perfect

gas, is gas, is // 1/t 1/tnn

There is an instant in the past where all the There is an instant in the past where all the matter and energy were concentrated in a matter and energy were concentrated in a

point...a singularity: the Big Bangpoint...a singularity: the Big Bang


Some common misconceptionsSome common misconceptions

The picture that the Universe expands into a The picture that the Universe expands into a preexisting space like an explosionpreexisting space like an explosion

The question “what was before the big The question “what was before the big bang?”bang?”

Remember: spacetime is part of the solution Remember: spacetime is part of the solution to Einstein’s equationto Einstein’s equation

Space and time are created in the big bangSpace and time are created in the big bang


So is the big crunch the same as So is the big crunch the same as the big bang run in reverse ?the big bang run in reverse ?

No. The Universe has meanwhile formed No. The Universe has meanwhile formed stars, black holes, galaxies etc.stars, black holes, galaxies etc.

Second law of thermodynamics:Second law of thermodynamics:The entropy (disorder) of a system at best The entropy (disorder) of a system at best stays the same but usually increases with stays the same but usually increases with time, in any process. There is no perpetual time, in any process. There is no perpetual motion machine.motion machine.

Second law of thermodynamics defines an Second law of thermodynamics defines an arrow of time.arrow of time.


At early epochs, the first term dominatesAt early epochs, the first term dominates the early universe appears to be almost flatthe early universe appears to be almost flat

• At late epochs, the second term dominatesAt late epochs, the second term dominates the late universe appears to be almost emptythe late universe appears to be almost empty

2

2

3

8

R

kcGH

2

2

3

8

R

kcGH

Friedmann’s equation for Friedmann’s equation for =0, =0, 00<1<1

Expansion rateExpansion rate

of the Universeof the UniverseFalls off like Falls off like

the cube of Rthe cube of R

Falls off like Falls off like

the square of Rthe square of R


At early epochs, the first term dominatesAt early epochs, the first term dominates the early universe appears to be almost flatthe early universe appears to be almost flat

• At late epochs, the third term dominatesAt late epochs, the third term dominates the late universe appears to be exponentially the late universe appears to be exponentially

expandingexpanding

33

82

2

R

kcGH

33

82

2

R

kcGH

Friedmann’s equation for Friedmann’s equation for >0, >0, 00<1<1

Expansion rateExpansion rate

of the Universeof the UniverseFalls off like Falls off like

the cube of Rthe cube of RFalls off like Falls off like

the square of Rthe square of R

constantconstant


The Expanding UniverseThe Expanding UniverseOn large scales, galaxies are moving apart,

with velocity proportional to distance.

It’s not galaxies moving through space.

Space is expanding, carrying the galaxies along!

The galaxies themselves are not expanding!


General acceptance of the big General acceptance of the big bang modelbang model

Until mid 60ies: big bang model very Until mid 60ies: big bang model very controversial, many alternative modelscontroversial, many alternative models

After mid 60ies: little doubt on validity of the After mid 60ies: little doubt on validity of the big bang modelbig bang model

Four pillars on which the big bang theory is Four pillars on which the big bang theory is resting:resting:– Hubble’s law Hubble’s law – Cosmic microwave background radiation Cosmic microwave background radiation – The origin of the elementsThe origin of the elements– Structure formation in the universeStructure formation in the universe


Georgy Gamov (1904-1968)Georgy Gamov (1904-1968)

If the universe is expanding, then If the universe is expanding, then there has been a big bangthere has been a big bang

Therefore, the early universe must Therefore, the early universe must have been very dense and hothave been very dense and hot

Optimum environment to breed the elements by Optimum environment to breed the elements by nuclear fusion (Alpher, Bethe & Gamow, 1948)nuclear fusion (Alpher, Bethe & Gamow, 1948)– success: predicted that helium abundance is 25%success: predicted that helium abundance is 25%– failure: could not reproduce elements more massive failure: could not reproduce elements more massive

than lithium and beryllium (than lithium and beryllium ( formed in stars) formed in stars)


What are the consequences ?What are the consequences ?In order to form hydrogen and helium at the right In order to form hydrogen and helium at the right proportions, the following conditions are required:proportions, the following conditions are required:– density:density: 10 10-5-5 g/cm g/cm-3-3 – temperature:temperature: T T 10 109 9 KK

Radiation from this epoch should be obser-vable as Radiation from this epoch should be obser-vable as an isotropic background radiationan isotropic background radiation

Due to the expansion of the universe to Due to the expansion of the universe to 331010-30-30 g/cmg/cm33, the temperature should have , the temperature should have dropped to dropped to T T 5 5 K (-268 C)K (-268 C)

Can we observe this radiation ?Can we observe this radiation ?


Penzias and Wilson 1965Penzias and Wilson 1965

Working at Bell labsWorking at Bell labs

Used a satellite dish to measure radio Used a satellite dish to measure radio emission of the Milky Wayemission of the Milky Way

They found some extra noise in the They found some extra noise in the receiver, but couldn’t explain itreceiver, but couldn’t explain it discovery of the background radiation discovery of the background radiation

Most significant cosmological observation Most significant cosmological observation since Hubblesince Hubble

Nobel prize for physics 1978Nobel prize for physics 1978


When does a gas become opaque?When does a gas become opaque?

A gas appears opaque (e.g. fog) if light is A gas appears opaque (e.g. fog) if light is efficiently scattered by the atoms/molecules of efficiently scattered by the atoms/molecules of the gasthe gas

The three important factors are thusThe three important factors are thus– the density of the gas the density of the gas

(denser (denser more particles more particles more scattering) more scattering)– the efficiency with which each individual particle can the efficiency with which each individual particle can

scatter lightscatter light– wavelength of the lightwavelength of the light


The transition from a transparent The transition from a transparent to an opaque universeto an opaque universe

At At zz=0=0 the universe is fairly transparent the universe is fairly transparent

At higher At higher zz, the universe becomes denser , the universe becomes denser (( = = 00(1+z)(1+z)33) and hotter () and hotter (T=TT=T00(1+z)(1+z)))

At At zz=1100=1100, the universe is so dense that its , the universe is so dense that its temperature exceeds 3000K. In a fairly sharp temperature exceeds 3000K. In a fairly sharp transition, the universe becomes completely transition, the universe becomes completely ionized and opaque to visible light. (last ionized and opaque to visible light. (last scattering surface)scattering surface)

At At zz=1100=1100, the universe is ~300 000 yrs old, the universe is ~300 000 yrs old


Proviamo a guardare Proviamo a guardare indietro nel tempo...indietro nel tempo...

-le distanze diminuiscono, tutto diventa piu’ denso, anchela densita’ di energia aumenta...

-Il primo evento drammatico che incontriamo andando all’indietro e’ successo quando l’Universo aveva un eta’ di ~300000 anni: la distanza fra le stelle (come le conosciamo oggi) diviene ~nulla: Tutto l’universo e’ composto dal materiale di cui sono composte le stelle...

-Questo e’ l’inizio dell’Universo visibile come lo conosciamo adesso...


Situazione a T<300 000 anniSituazione a T<300 000 anniin quelle condizioni di

densita’, tutto l’Universo aveva la temperatura della

superficie di una stella (>3000 K): non esistono atomi neutri

etanta luce (fotoni) in interazione con la materia

carica elettricamente La luce e’ intrappolata! non puo’ arrivarci nessun

raggio luminoso da epoche per cui T< 300 000 anni...

(altre particelle in principio possono: i neutrini per esempio)

Si ha equilibrio tra radiazione e materia spettro di corpo nero


pero’, a causa dello “stiramento” dello spazio la sua lunghezza d’onda aumenta (e l’energia

diminuisce: si raffredda...)

Situazione a T~300 000 anni

con l’espansione dell’universo T diventa <3000 K, gli elettroni si legano ai protoni per formare

atomi neutri di H non c'e' piu' interazione luce-materia: I

fotoni cominciano a propagarsi liberamente (materia poco

densa) e devono continuare tuttora: Disaccoppiamento radiazione-

materiaLa radiazione prima intrappolata e' ora libera di propagarsi nello spazio e giungere fino a noi ci si

aspetta che esista una radiazione uniforme che "riempe" tutto l'universo


Looking Back Towards the Early UniverseLooking Back Towards the Early Universe

The more distant the objects we observe, the further back into the past of the universe we are looking.

trasparent

opaque


Black body radiationBlack body radiation

A hot a body is brighter than a cool one A hot a body is brighter than a cool one ((LLTT44, , Stefan-Boltzmann’s lawStefan-Boltzmann’s law))

A hot body’s spectrum is bluer than that A hot body’s spectrum is bluer than that of a cool one (of a cool one (maxmax1/1/TT, , Wien’s lawWien’s law))


The cosmic microwave The cosmic microwave background radiation (CMB)background radiation (CMB)

Temperature of Temperature of 2.728±0.004 K2.728±0.004 K

isotropic to isotropic to 1 part in 100 0001 part in 100 000

perfect black bodyperfect black body

1990ies: CMB is 1990ies: CMB is one of the major tools to study cosmologyone of the major tools to study cosmology

Note: ~1% of the noise in your TV is from Note: ~1% of the noise in your TV is from the big bangthe big bang


Emissione di radiazione elettromagnetica da un corpo

Alla temperatura di 37 gradi centigradi (circa 310 gradi kelvin) l’emissione è concentrata nell’infrarosso


Should the CMB be perfectly Should the CMB be perfectly smooth ?smooth ?

No. Today’s Universe No. Today’s Universe is homogeneous and is homogeneous and isotropic on the largest isotropic on the largest scales, but there is a scales, but there is a fair amount of structure fair amount of structure on small scales, such on small scales, such as galaxies, clusters of as galaxies, clusters of galaxies etc.galaxies etc.


L’esistenza di questa radiazione primordiale e’ la prova diretta che l’Universo in qualche momento del passato era qualitativamente diverso da quello attuale.

Permette di “fotografare” l’Universo quando aveva “soltanto” ~300000 anni...

Tutt’oggi continuiamo ad imparare tantissimo dallo studio ad alta precisione di questa radiazione

Curiosita’: ~ l’1% dell’effetto “neve” nei TV e’ dato dal fondodi radiazione cosmica

CMB : Cosmic Microwave BackgroundCBR: Cosmic Background Radiation

400 fotoni/cm3


Should the CMB be perfectly Should the CMB be perfectly smooth ?smooth ?

We expect some We expect some wriggles in the CMB wriggles in the CMB radiation, radiation, corresponding to the corresponding to the seeds from which later seeds from which later on galaxies growon galaxies grow


The Cosmic Background The Cosmic Background Explorer (COBE)Explorer (COBE)

Main objectives:Main objectives:

To accurately To accurately measure the measure the temperature of the temperature of the CMBCMB

To find the To find the expected expected fluctuations in the fluctuations in the CMBCMB


Main results from COBEMain results from COBE


More results from the CMBMore results from the CMB

The Earth is moving The Earth is moving with respect to the with respect to the CMB CMB Doppler shift Doppler shift– Earth’s motion around Earth’s motion around

the Sunthe Sun– Sun’s motion around Sun’s motion around

the Galaxythe Galaxy– Motion of the Galaxy Motion of the Galaxy

with respect to other with respect to other galaxies (large scale galaxies (large scale flows)flows)



The Earth is moving The Earth is moving with respect to the with respect to the CMB CMB Doppler shift Doppler shift

The emission of the The emission of the GalaxyGalaxy



The Earth is moving The Earth is moving with respect to the CMB with respect to the CMB Doppler shift Doppler shift

The emission of the The emission of the GalaxyGalaxy

Fluctuations in the CMBFluctuations in the CMB


Where do the CMB fluctuations Where do the CMB fluctuations come from ?come from ?

Wrinkles: some regions have a slightly Wrinkles: some regions have a slightly higher gravity, some a slightly lower higher gravity, some a slightly lower (“potential wells”)(“potential wells”)

Matter falls into potential wellsMatter falls into potential wells


Competition between gravity (pull in) and Competition between gravity (pull in) and pressure (push out) pressure (push out) oscillations oscillations

““The Sound of the Universe”The Sound of the Universe”

What happens to the infalling gas?What happens to the infalling gas?


Can we see the sound of the Can we see the sound of the universe ?universe ?

Compressed gas heats upCompressed gas heats up

temperature fluctuations temperature fluctuations


Measuring the Curvature of the Measuring the Curvature of the Universe Using the CMBUniverse Using the CMB

Sound waves Sound waves universe is a resonator universe is a resonator

lowest pitch: lowest pitch: fundamental mode fundamental mode resonatesresonates

fundamental mode: fundamental mode: distance sound can distance sound can travel over the age travel over the age of the universe of the universe (@ z=1100) (@ z=1100) it depends on it depends on : : llpeakpeak=220=220oo//

angleangle


The Music of the UniverseThe Music of the Universe



Recall: with Recall: with supernovae, one supernovae, one measures measures qq00 =½ =½00 – –

CMB fluctuations CMB fluctuations measure curvaturemeasure curvature 00 + +

two equations for two two equations for two variablesvariables problem solved problem solved


The universe contentThe universe contentThe results:The results:

The Universe is The Universe is flat:flat:tottot=1=1§§ 0.1 0.1

»»30% is matter30% is matter

70% is cosmological 70% is cosmological constant, the so-constant, the so-called "dark energy"called "dark energy"

Dark energy: we know is there, but have not

idea of what it is


Se ne conclude che:

1. L’Universo è dominato da una forma sconosciuta di energia

2. La maggioranza della MATERIA è OSCURA

3. La maggioranza della materia oscura (DM) è diversa da quella ordinaria

Contributi ad da:

1. Materia ) m

2. Radiazione ) r

3. Energia del vuoto ) Quali sono le stime attuali?

Stima dei parametri cosmologici

TOT=1.02§0.2

r»O(10-5) =0.73§0.04m=0.27§0.04

lum<0.006 B=0.044§0.004 ??


The early Universe: The early Universe: Cooking the helium in Cooking the helium in

the Universe -the Universe -the Big Bang the Big Bang

nucleosynthesisnucleosynthesis



After mid 60ies: little doubt on validity of After mid 60ies: little doubt on validity of the big bang modelthe big bang model

Four pillars on which the big bang theory Four pillars on which the big bang theory is resting:is resting:– Hubble’s law Hubble’s law – Cosmic microwave background radiationCosmic microwave background radiation– The origin of the elementsThe origin of the elements– Structure formation in the universeStructure formation in the universe




Four pillars on which the big bang theory Four pillars on which the big bang theory is resting:is resting:– Hubble’s law Hubble’s law – Cosmic microwave background radiation Cosmic microwave background radiation – The origin of the elementsThe origin of the elements– Structure formation in the universeStructure formation in the universe


Georgy Gamov (1904-1968)Georgy Gamov (1904-1968)

If the universe is expanding, then If the universe is expanding, then there has been a big bangthere has been a big bang

Therefore, the early universe must Therefore, the early universe must have been very dense and hothave been very dense and hot

Optimum environment to breed the elements by Optimum environment to breed the elements by nuclear fusion (Alpher, Bethe & Gamow, 1948)nuclear fusion (Alpher, Bethe & Gamow, 1948)– success: predicted that helium abundance is 25%success: predicted that helium abundance is 25%– failure: could not reproduce elements more massive failure: could not reproduce elements more massive

than lithium and beryllium (than lithium and beryllium ( formed in stars) formed in stars)


Particle and nuclear physicsParticle and nuclear physics

Particle physics joins cosmologyParticle physics joins cosmology

In the hot and dense young Universe In the hot and dense young Universe high energy particles have enough high energy particles have enough energy to undergo to processes energy to undergo to processes governed by elementary particle physics governed by elementary particle physics (quantum) laws as T(quantum) laws as T11


La nostra attuale comprensione La nostra attuale comprensione delle interazioni fondamentali delle interazioni fondamentali delle particlle elementari e’ delle particlle elementari e’

riassunta da quello che riassunta da quello che chiamiamo:chiamiamo:

esso descrive sia la materia che tutte le forze che la governano. La sua bellezza sta nella

capacità di spiegare centinaia di particelle e interazioni complesse con poche particelle e

interazioni (forze) fondamentali.


2) 3 tipi di costituenti: 3 tipi di costituenti:

a) quarks (6 x 3 x 2)

b) elettroni, neutrini e simili (“leptoni”) (6 x 2)

c) particelle “mediatrici delle forze”: gravitoni, fotoni, gluoni, bosoni (13)

1) 4 tipi di forze (ma in via di unificazione) 4 tipi di forze (ma in via di unificazione)

1) nucleare forte

2) nucleare debole

3) elettromagnetica

4) gravitazionale

particelle + antiparticelle

elettrodebole

In tale modello: In tale modello:


Ecco tutte le interazioni in breve....

L’ aspetto entusiasmante della moderna visioneL’ aspetto entusiasmante della moderna visionee’ che e’ che camminiamo nella direzione di una descrizionecamminiamo nella direzione di una descrizione

unificata delle forzeunificata delle forze

Siamo gia’ in grado di parlare di Siamo gia’ in grado di parlare di forza elettro-debole invece che di forza elettro-debole invece che di

debole ed elettro-magnetica separatamente!!!debole ed elettro-magnetica separatamente!!!

Arriveremo mai alla “Grande Unificazione”??Arriveremo mai alla “Grande Unificazione”??

(M=0 , S = 2)(M=0 , S = 2)

(M~90 GeV/c(M~90 GeV/c22 , S = 1) , S = 1)

(M=0 , S = 1)(M=0 , S = 1)

(M=0 , S = 1)(M=0 , S = 1)


The structure of matterThe structure of matter

Atoms are mostly empty spaceAtoms are mostly empty space

Atoms consist of protons (+), neutrons (o) and Atoms consist of protons (+), neutrons (o) and electrons (-)electrons (-)

protons and neutrons protons and neutrons form the atomic form the atomic nucleusnucleus

# of protons deter-# of protons deter-mines the elementmines the element

electrons in the outskirts determine chemistryelectrons in the outskirts determine chemistry

Protoni, neutroni

quarks


The structure of matterThe structure of matter

Neutrons and protons are very similar, butNeutrons and protons are very similar, but– Protons are electrically charged, neutrons are notProtons are electrically charged, neutrons are not– Neutrons have a slightly higher massNeutrons have a slightly higher mass

Electrons are much less massive than Electrons are much less massive than nucleons nucleons most of the mass of an atom is in most of the mass of an atom is in its nucleusits nucleus

If charges of the same sign repel, and the If charges of the same sign repel, and the nucleus is made of protons, why don’t the nucleus is made of protons, why don’t the protons fly apart ?protons fly apart ?


Breve cronistoria dell’universo alla luce della nostra Breve cronistoria dell’universo alla luce della nostra conoscenza attuale delle forze e della materia: conoscenza attuale delle forze e della materia:

il modello cosmologico standardil modello cosmologico standard

- Il modello standard della fisica ci permettono di estrapolare la descrizione dell’Universo per t<105 anni

-Fino a quando la densita’ e tale che le particelle di cui e’ costituita la materia perdono la loro identita’...

-Fino a ~ il “Tempo 0” (il “Big Bang”) ma non proprio...

Questo esercizio pero’ di puo’ fare con incertezze tantomaggiori tanto piu’ ci avviciniamo a t=0!

Cosa c’era prima? La domanda non ha senso. Come conseguenzadella R.G., spazio e tempo non esistevano prima, non c’e’ statoun prima! (anche S. Agostino c’era arrivato...)


Abundance of elementsAbundance of elements

Hydrogen and helium Hydrogen and helium most abundantmost abundant

gap around Li, Be, Bgap around Li, Be, B

Where do they come from?


Thermal history of the universeThermal history of the universeWhen the universe was younger than When the universe was younger than 300 000 yrs, it was so hot that neutral atoms 300 000 yrs, it was so hot that neutral atoms separated into nuclei and electrons. It was too separated into nuclei and electrons. It was too hot to bind atomic nuclei and electrons to atoms hot to bind atomic nuclei and electrons to atoms by the electromagnetic force by the electromagnetic force

When the universe was younger than When the universe was younger than ~1 sec, it was so hot that atom nuclei separated ~1 sec, it was so hot that atom nuclei separated into neutrons and protons. It was too hot to bind into neutrons and protons. It was too hot to bind protons and neutrons to atomic nuclei by the protons and neutrons to atomic nuclei by the strong nuclear force strong nuclear force


Formation of helium in the big bangFormation of helium in the big bang

HydrogenHydrogen: 1 nucleon (proton): 1 nucleon (proton)

HeliumHelium:: 4 nucleons (2 protons, 2 neutrons) 4 nucleons (2 protons, 2 neutrons)

In order to from helium from hydrogen one has toIn order to from helium from hydrogen one has to– bring 2 protons and 2 neutrons close together, so the bring 2 protons and 2 neutrons close together, so the

strong nuclear force can act and hold them togetherstrong nuclear force can act and hold them together– close together: Coulomb repulsion has to be close together: Coulomb repulsion has to be

overcome overcome high velocities high velocities high temperatures high temperatures

but: but: 4 body collisions are highly unlikely4 body collisions are highly unlikely


Transforming hydrogen into heliumTransforming hydrogen into helium

Hot big bang: Hot big bang: neutronsneutrons and and protonsprotons

Use a multi step procedure:Use a multi step procedure:– p + n p + n 22H H – p + p + 22H H 33HeHe– n + n + 22H H 33HH– 33He + He + 33He He 44He + 2 pHe + 2 p

some side reactions:some side reactions:– 33He + He + 33H H 77Li Li – 33He + He + 33He He 77Be Be


Mass gap/stability gap at A=5 Mass gap/stability gap at A=5 and 8and 8

There is no stable atomic nucleus with 5 There is no stable atomic nucleus with 5 or with 8 nucleonsor with 8 nucleons

Reaction chain stops at Reaction chain stops at 77LiLi

So how to form the more massive So how to form the more massive elements?elements?

There exist a meta-stable nucleus (There exist a meta-stable nucleus (88B*B*). ). If this nucleus is hit by another If this nucleus is hit by another 44HeHe during its lifetime, during its lifetime, 1212CC and other and other elements can be formedelements can be formed


Mass gap/stability gap at A=5 Mass gap/stability gap at A=5 and 8and 8

Reaction chain:Reaction chain:– 44He + He + 44He He 88B* B* – 88B* + B* + 44He He 1212CC

so-called 3-body reactionso-called 3-body reaction

in order to have 3-body reactions, high particle in order to have 3-body reactions, high particle densities are requireddensities are required– densities are not high enough in the big-bangdensities are not high enough in the big-bang– but they are in the center of evolved starsbut they are in the center of evolved stars

Conclusion: big bang synthesizes elements up to Conclusion: big bang synthesizes elements up to 77Li. Higher elements are formed in starsLi. Higher elements are formed in stars


Primordial nucleosynthesisPrimordial nucleosynthesis

Result:Result:

abundance of abundance of

H,He and Li is consistentH,He and Li is consistent

but:but: bb ~0.04 while the ~0.04 while the tottot content is 0.3 content is 0.3

Consistent with Consistent with

abundanceabundance

of H, He and Liof H, He and Li


Can we understand why 25% He?Can we understand why 25% He?

Before the universe cooled sufficiently to Before the universe cooled sufficiently to allow nucleons to assemble into helium, the allow nucleons to assemble into helium, the neutron to proton ratio was 1:7neutron to proton ratio was 1:744He:He: equal number of protons and neutrons equal number of protons and neutrons

Assume that all neutrons grab a proton to Assume that all neutrons grab a proton to form a form a 44HeHe. The left over protons form . The left over protons form hydrogen.hydrogen.


n

nnX n

H

*2 75.0

7/8

7/6

/1

/1*2

pn

pn

np

npnH nn

nn

nn

nn

n

nnX

Can we understand why 25% He?Can we understand why 25% He?Abundance of hydrogenAbundance of hydrogenAbundance of hydrogenAbundance of hydrogen

Abundance of helium: Abundance of helium: 1-0.75 = 0.251-0.75 = 0.25

butbut why is why is nnnn/n/npp = 1/7= 1/7 ? ?


Less than 1 second after the Big Bang, the reactions shown maintain the neutron:proton ratio in thermal equilibrium. About 1 second after the Big Bang, the temperature is slightly less than the neutron-proton mass difference, these weak reactions become slower than the expansion rate of the Universe, and the neutron:proton ratio freezes out at about 1:7


What happened when the What happened when the universe was even younger?universe was even younger?

Recall special relativity: Recall special relativity: E=mcE=mc22

If the thermal energy exceeds twice the rest If the thermal energy exceeds twice the rest mass energy of a particle, mass energy of a particle, particle-antiparticle pairs can be created particle-antiparticle pairs can be created Pair creationPair creation

Matter:Matter: protons, neutrons, electrons protons, neutrons, electrons neutrinosneutrinos

Antimatter:Antimatter: antiprotons, antineutrons, antiprotons, antineutrons, positrons, antineutrinopositrons, antineutrino


Pair creationPair creation

Antiparticle: same mass as particle, but Antiparticle: same mass as particle, but opposite charge.opposite charge.

Antimatter has positive mass !!!!!!Antimatter has positive mass !!!!!!

ee++

ee--

The inverse process is called annihilationThe inverse process is called annihilation


ExamplesExamples

T>10T>101010 K: creation/annihilation of electron- K: creation/annihilation of electron-positron pairspositron pairs

T>10T>101313 K: creation/annihilation of proton- K: creation/annihilation of proton-antiproton pairsantiproton pairs


A common theme ...A common theme ...

For each reaction there is a temperature For each reaction there is a temperature TTcc::

– For temperature larger thanFor temperature larger than TTcc, there is a , there is a

continuous transformation between photons into continuous transformation between photons into particle-antiparticle pairs and vice versaparticle-antiparticle pairs and vice versa

– This state is calledThis state is called thermal equilibriumthermal equilibrium – If the temperature drops below the threshold If the temperature drops below the threshold

temperaturetemperature TTcc, pair creation, pair creation freezes outfreezes out, ,

remaining pairs annihilate.remaining pairs annihilate.


The thermal history of the The thermal history of the UniverseUniverse


t = 15 109 anni: vita , noi, ora, T = 3 K

t = 5 109: anni galassie

t = 1 109 anni: Proto-galassie

t = 3 105 anni: Disaccoppiamento materia-radiazione T=3000 K

t = 104 anni: Inizia l’era dominata dalla materia T= 1.8 104 K

era della materia

The energy of matter is nowadays ~10000 times higher The energy of matter is nowadays ~10000 times higher than that of radiationthan that of radiation

but temperature rises like but temperature rises like (1+z)(1+z)

2.7K < T < 10000K2.7K < T < 10000K: matter era: matter era

dominate particles (in order of decreasing contribution:dominate particles (in order of decreasing contribution:– baryonsbaryons, photons, neutrinos, photons, neutrinos

dominant forces:dominant forces:– gravitygravity







t = 180 s: Nucleosintesi T=7.5 108 K

t = 1 s: Annichilazione elettroni-positroni T=1010 K

era della radiazione

era della materia

As the temperature exceeds ~ 10000K, radiation starts dominatingAs the temperature exceeds ~ 10000K, radiation starts dominating

10000K < T < 1010000K < T < 101010KK: radiation era: radiation era

dominate particles (in order of decreasing contribution:dominate particles (in order of decreasing contribution:

– photons, neutrinosphotons, neutrinos, baryons, baryons

dominant forces:dominant forces:

– electromagnetismelectromagnetism, gravity, gravity










era della materia

As the temperature exceeds ~ 10As the temperature exceeds ~ 101010K, creation of electron-positron pairsK, creation of electron-positron pairs

– T > 10T > 101010K: equilibrium between electron-positron pair creation and K: equilibrium between electron-positron pair creation and annihilationannihilation

– T < 10T < 101010K: freeze-out. Remaining pairs annihilateK: freeze-out. Remaining pairs annihilate








t = 1 s: Annichilazione elettroni-positroni T=1010 Kt ~ 10-4 s: Era “leptonica”

t < 10-6 s: i quarks si combinano in p e n T=1013 K


era della materia

Hadron hannihilation: As the temperature exceeds ~ 10Hadron hannihilation: As the temperature exceeds ~ 101212K, creation K, creation of hadron-antihadron pairs (e.g. proton-antiproton)of hadron-antihadron pairs (e.g. proton-antiproton)– T > 10T > 101212K: equilibrium between hadron pair creation and K: equilibrium between hadron pair creation and

annihilationannihilation– T < 10T < 101212K: freeze-out. Remaining pairs annihilateK: freeze-out. Remaining pairs annihilate








t = 1 s: Annichilazione elettroni-positroni T=1010 Kt ~ 10-4 s: Era “leptonica”

t < 10-6 s: i quarks si combinano in p e n T=1013 K


era della materia

Hadron era: 10Hadron era: 101212KK < T << T < 10101313KK

dominant particles (in order of decreasing contribution:dominant particles (in order of decreasing contribution:– baryons+antiparticles, mesons+antiparticles, electrons, baryons+antiparticles, mesons+antiparticles, electrons,

positrons, photons, neutrinos, antineutrinospositrons, photons, neutrinos, antineutrinos

dominant forces:dominant forces:– electromagnetism, strong nuclear, weak nuclearelectromagnetism, strong nuclear, weak nuclear, gravity, gravity

Quark era:10Quark era:101313KK < T << T < 10101515KK

hadrons (baryons, mesons) break into quarkshadrons (baryons, mesons) break into quarks

dominate particles (in order of decreasing contribution:dominate particles (in order of decreasing contribution:– quarks, antiquarks, e- e+, photons, neutrinos, antineutrinosquarks, antiquarks, e- e+, photons, neutrinos, antineutrinos

dominant forces:dominant forces:– electromagnetism, strong nuclear, weak nuclearelectromagnetism, strong nuclear, weak nuclear, gravity, gravity









t ~ 10-10 s: Separazione forza elettro-debole T=1015 K

t ~ 10-4 s: Era “leptonica”t < 10-6 s: i quarks si combinano in p e n T=1013 K


era della materiaElectroweak phase transition: As the temperature Electroweak phase transition: As the temperature exceeds ~ 10exceeds ~ 101515K, electromagnetism and weak nuclear K, electromagnetism and weak nuclear force join to form the electroweak forceforce join to form the electroweak force– T > 10T > 101515K: electroweak forceK: electroweak force– T < 10T < 101515K: electromagnetism, weak nuclear forceK: electromagnetism, weak nuclear force

Limit of what we can test in particle accelerators.Limit of what we can test in particle accelerators.

Nobel prizes 1979 (theory) and 1984 (experiment)Nobel prizes 1979 (theory) and 1984 (experiment)












era della materia

10101515KK < T << T < 10102929KK

dominate particles (in order of decreasing contribution:dominate particles (in order of decreasing contribution:– quarks, antiquarks, electrons, positrons, photons, neutrinos, quarks, antiquarks, electrons, positrons, photons, neutrinos,

antineutrinosantineutrinos

dominant forces:dominant forces:– electroweak, strong nuclearelectroweak, strong nuclear, gravity, gravity












t < 10-36 s: “Era della Grande Unificazione” T=1028 K

era della materia

GUT phase transition: As the temperature exceeds ~ 10GUT phase transition: As the temperature exceeds ~ 102929K, K, electroweak force and strong nuclear force join to form the GUT electroweak force and strong nuclear force join to form the GUT (grand unified theories)(grand unified theories)– T > 10T > 102929K: GUTK: GUT– T < 10T < 102929K: electroweak force, strong nuclear forceK: electroweak force, strong nuclear force

relatively solid theoretical framework (but may be wrong), but pretty relatively solid theoretical framework (but may be wrong), but pretty much no constraint by experimentsmuch no constraint by experiments

GUT era: 10GUT era: 102929KK < T << T < 10103232KK

dominate particles (in order of decreasing contribution:dominate particles (in order of decreasing contribution:– Zillions of particles, most of them not detected yet Zillions of particles, most of them not detected yet

dominant forces:dominant forces:– GUTGUT, gravity, gravity









t = 10-43 s: Tempo di PlancK: Limite della fisica moderna




t < 10-36 s: “Era della Grande Unificazione” T=1028 K

era della materiaPlanck epoch: T > 10Planck epoch: T > 103232K unification of K unification of GUT and gravityGUT and gravity

Particles:Particles:– ??????

Forces:Forces:– TOE (theory of everything)TOE (theory of everything)

The last frontier ...The last frontier ...


T»100 GeVt»10-10 s




Four pillars on which the big bang theory Four pillars on which the big bang theory is resting:is resting:– Hubble’s law Hubble’s law – Cosmic microwave background radiation Cosmic microwave background radiation – The origin of the elementsThe origin of the elements – Structure formation in the universeStructure formation in the universe



Structure formation in the Big-Structure formation in the Big-Bang modelBang model


The Hubble sequence of The Hubble sequence of galaxiesgalaxies


Younger galaxies should be Younger galaxies should be smaller ...smaller ...


How good is the assumption of How good is the assumption of isotropy?isotropy?

CMB: almost perfectCMB: almost perfect

but what about the closer neighborhood ?but what about the closer neighborhood ?


How good is the assumption of How good is the assumption of isotropy?isotropy?

CMB: almost perfectCMB: almost perfect

but what about the closer neighborhood ?but what about the closer neighborhood ?

The great The great

wallwall


Galaxies are not Galaxies are not randomly distributed but randomly distributed but correlatedcorrelated

Network of structures Network of structures (filaments, sheets, (filaments, sheets, walls) walls) “cosmic web” “cosmic web”

The spatial distribution of galaxiesThe spatial distribution of galaxies

Courtesy: Huan LinCourtesy: Huan Lin


How does structure form ?How does structure form ?

Wrinkles in the CMB: regions of higher and Wrinkles in the CMB: regions of higher and lower temperaturelower temperature

Those regions correspond to Those regions correspond to density density fluctuationsfluctuations, regions of slightly higher/lower , regions of slightly higher/lower density than averagedensity than average

Gravitational instabilityGravitational instability– higher density higher density more mass in a given volume more mass in a given volume– more mass more mass stronger gravitational attraction stronger gravitational attraction– stronger gravitational attraction stronger gravitational attraction mass is pulled in mass is pulled in even higher density even higher density


z=9.00z=9.00

65 M

pc65

Mpc

50 million 50 million particle particle N-body N-body simulationsimulation


z=4.00z=4.00

65 M

pc65

Mpc



z=2.33z=2.33

65 M

pc65

Mpc



z=1.00z=1.00

65 M

pc65

Mpc



z=0.00z=0.00

65 M

pc65

Mpc



Sommario della nuova cosmologia:Sommario della nuova cosmologia:si fonda su 3 fatti/osservazioni si fonda su 3 fatti/osservazioni

1 postulato + 1 modello di 1 postulato + 1 modello di riferimentoriferimento

1) su larga scala l’universo e’ lo stesso in tutte le direzioni (isotropia)

2) piu’ guardiamo indietro nel tempo (lontano da noi) piu’ l’universo appare diverso dal nostro: in particolare era molto “caldo” (CMB)

3) tanto piu’ un oggetto e’ lontano, tanto piu‘ sembra allontanarsi velocemente da noi (legge di Hubble)

Congettura: la porzione di universo in cui noi siamo

non ha nulla di speciale (Principio Cosmologico)

Modello di riferimento: La Relativita’ Generale


Riassumendo: Riassumendo: i successi del modello cosmologico i successi del modello cosmologico

standard standard (il Big Bang)(il Big Bang)

1) Spiegazione dell’esistenza del CMB

2) Previsione quantitativa dell’abbondanza di elementi leggeri (idrogeno, deuterio, elio, litio) nell’universo in accordo con le misure

3) spiegazione delle strutture su larga scala delle galassie in connessione con le piccole irregolarita’ del CMB

Ma il modello standard non e’ piu’ sufficiente...


How can we measure How can we measure massmass ? ?

Count all the mass we can “see”Count all the mass we can “see”– tricky, some of the mass may be hidden …tricky, some of the mass may be hidden …

Using Kepler’s third law: measure the Using Kepler’s third law: measure the dynamics of a system and apply Kepler’s law dynamics of a system and apply Kepler’s law to infer the massto infer the mass– for hot systemsfor hot systems (elliptical galaxies, clusters of (elliptical galaxies, clusters of

galaxies): measure the velocity dispersion galaxies): measure the velocity dispersion (random velocity) of the constituents(random velocity) of the constituents

– for cold systemsfor cold systems (disk galaxies): measure the (disk galaxies): measure the velocity at which stars orbitvelocity at which stars orbit


Counting all the mass ...Counting all the mass ...

Obstacle: Obstacle: we want mass, but we see lightwe want mass, but we see light

Procedure:Procedure:– count all the stars you see and multiply them count all the stars you see and multiply them

with there luminosity with there luminosity total visible luminosity total visible luminosity– correct for dust absorption correct for dust absorption total luminosity total luminosity– convert luminosity into mass using a mass-to-convert luminosity into mass using a mass-to-

light ratiolight ratio

– The sun has The sun has =1=1 by definition. by definition.

sun

sun

LL

MM

/

/

sun

sun

LL

MM

/

/


Visible mass in the Universe:Visible mass in the Universe:

Implications:Implications:

less than the nucleosynthesis constraint of less than the nucleosynthesis constraint of barybary=0.04 =0.04 in baryons in baryons consistent consistent

Most of the baryons in the universe (~75%) do not Most of the baryons in the universe (~75%) do not shine [are too dim to be detected] shine [are too dim to be detected] – gas and dustgas and dust– stellar remnants (white dwarfs, neutron stars, black holes)stellar remnants (white dwarfs, neutron stars, black holes)– brown dwarfs [failed stars]brown dwarfs [failed stars]

01.0 01.0


Le scoperte piu’ recentiLe scoperte piu’ recenti

C’e un nuovo tipo di materia che non conosciamo:Dall'analisi degli effetti gravitazionali, si puo’ stabilire che esiste anche un tipo di materia che noi non possiamo vedere (non prodice luce), anzi la maggior parte dell'universo sembra non sia dello stesso tipo di materia di cui sono fatte le stelle (protoni-neutroni-elettroni).

Materia non oscura Materia oscura

La chiamiamo "materia oscura"


The Problem of Dark MatterThe Problem of Dark Matter- Observed from gravitational interactions only!- Observed from gravitational interactions only!

Galactic Rotation Curves

Alle

n, Schm

idt, Fabian (20

02)

Observe galaxy rotation curve using Observe galaxy rotation curve using Doppler shifts in 21 cm line from hyperfine Doppler shifts in 21 cm line from hyperfine splittingsplitting

Virtually all galaxies have a dark halo

Luminous matter cannot account for the observed rotation curves There must be a dark a nearly

spherical halo

Expected from luminous mass

Observed A halo of non-luminous matter must be added to account for the observed

radial speed


Materia oscuraMateria oscura


Let’s use some numbers ...Let’s use some numbers ...A galaxy like the Milky Way or Andromeda has a A galaxy like the Milky Way or Andromeda has a total visible mass of about total visible mass of about 6610101010 M Msunsun..

The rotation velocity is The rotation velocity is ~220 km/sec~220 km/sec

The radius about The radius about ~30 kpc~30 kpc

Newton:Newton:

total mass: total mass: 3.33.310101111 M Msunsun

~5 times more mass than visible ~5 times more mass than visible

G

RvM

R

GMv

2rot

rot G

RvM

R

GMv

2rot

rot


Dark Matter in Galaxy ClustersDark Matter in Galaxy Clusters

Galaxies form clusters bound Galaxies form clusters bound in a gravitational wellin a gravitational well

Hydrogen gas in the well get Hydrogen gas in the well get heated, emit X-rayheated, emit X-ray

Can determine baryon fraction Can determine baryon fraction of the clusterof the cluster

ffBBhh3/23/2=0.056=0.0560.0140.014

Combine with the BBNCombine with the BBN

mattermatterhh1/21/2=0.38=0.380.070.07

Agrees with SZ, virialAgrees with SZ, virial

Zwicky, Helv. Phys. Acta 6 (1933) Zwicky, Helv. Phys. Acta 6 (1933) 110110

Coma cluster

the most part of cluster gravitational mass is dark


Evidence of dark matter: Evidence of dark matter: X-ray clusters X-ray clusters


Evidence of dark matter: Evidence of dark matter: clusters of galaxies clusters of galaxies


Evidence of dark matter: Evidence of dark matter: large scale flowslarge scale flowsEvidence of dark matter: Evidence of dark matter: large scale flowslarge scale flows


Overall result:Overall result:

Implications:Implications:

most of the mass in the Universe is darkmost of the mass in the Universe is dark

most of it is even of non-baryonic originmost of it is even of non-baryonic origin

the perfect Copernican principlethe perfect Copernican principle– The Earth is not at the center of the solar systemThe Earth is not at the center of the solar system– The Sun is not at the center of the Milky WayThe Sun is not at the center of the Milky Way– The Milky Way is not at the center of the UniverseThe Milky Way is not at the center of the Universe– We may not even be made from the most abundant type of We may not even be made from the most abundant type of

matter in the Universe matter in the Universe

3.0 3.0 But lum = 0.001 and BBN =0.04


~90% of the mass in the ~90% of the mass in the Universe is of some sort of Universe is of some sort of

invisible (dark) matter, invisible (dark) matter, probably even of quite probably even of quite

different nature than the stuff different nature than the stuff we are made of.we are made of.


90% dark matter ?90% dark matter ?These astronomers must be These astronomers must be

crazy !crazy !


Is the claim that dark matter exist Is the claim that dark matter exist really so embarrassing ?really so embarrassing ?

When Leverrier was proposing in When Leverrier was proposing in the 1840s that there maybe anthe 1840s that there maybe an8th planet in the solar system,8th planet in the solar system,NeptuneNeptune, a planet that can explain , a planet that can explain the irregularities of Uranus’ orbit,the irregularities of Uranus’ orbit,this planet was also this planet was also “dark matter”“dark matter”

But it was a clear prediction that eventually But it was a clear prediction that eventually could be tested observationallycould be tested observationally

The discovery of The discovery of NeptuneNeptune by Galle was one of by Galle was one of the finest moments of science the finest moments of science


Occorre cambiare il “Modello Standard” delle particelle!

Tra le nuove proposte una delle idee piu’ promettentiTra le nuove proposte una delle idee piu’ promettentie’ quella della unificazione di tutte le forzee’ quella della unificazione di tutte le forzenel quadro della nel quadro della “SuperSimmetria”“SuperSimmetria”

Ad ogni particella che conosciamo ne corrisponde Ad ogni particella che conosciamo ne corrisponde una “ombra” (e viceversa) molto pesante...una “ombra” (e viceversa) molto pesante...

ad ogni ad ogni quarkquark corrisponde uno corrisponde uno s-quarks-quark(s sta per “shadow”)(s sta per “shadow”)

ad ogni ad ogni leptoneleptone corrisponde uno corrisponde uno s-leptones-leptone

Ad ogni bosone mediatore Ad ogni bosone mediatore ...one...onecorrisponde un corrisponde un ...ino...inoEs.: Es.: fotone fotone fotino fotino

Una delle particelle della supersimmetria, il "neutralino" potrebbe essere quella che compone la massa mancante dell’universo. Forse è fatta di neutrini, o magari di altre forme materiali ancora più insolite...


I problemi non risolti I problemi non risolti dal modello cosmologico dal modello cosmologico

standardstandardIl problema della “piattezza” e dell’eta’ dell’universo

Come e’ possibile realizzare la stupefacente uniformita’del fondo di radiazione? Come si possono “parlare”

fra loro delle zone di universo che non sono in“connessione causale”?

I dati osservativi indicano una densita’ media dell’Universo vicinissima al “valore critico”

(implica k~0)Bastava poca materia in piu’ per far “morire” (collassare)

l’universo molto prima

Il problema dell’orizzonte


I problemi non risolti I problemi non risolti dal modello cosmologico dal modello cosmologico

standardstandardIl problema della “piattezza” e dell’eta’ dell’universo

Come e’ possibile realizzare la stupefacente uniformita’del fondo di radiazione? Come si possono “parlare”

fra loro delle zone di universo che non sono in“connessione causale”?

I dati osservativi indicano una densita’ media dell’Universo vicinissima al “valore critico”

(implica k~0)Bastava poca materia in piu’ per far “morire” (collassare)

l’universo molto prima




Se D> c Tuniverso come possono A e B scambiarsi informazioni?

DA B


Un nuovo paradigma: L’ Un nuovo paradigma: L’ “Inflazione” “Inflazione”

(universo gonfiato)(universo gonfiato)

A. Guth, 1980

L’ universo che vediamo puo’ venire da una porzione infinitesimamente piccola dell’universo primordiale che si

e’ espansa per un breve periodo a velocita’ molto superiore aquella della luce (possibile anche in Relativita’ !)

Meccanismo (molto complesso): prima della formazione

di quarks e leptoni, si crea uno stato speciale (“falso vuoto”) che fornisce una enorme

accelerazione...


Espansione “normale”

Espansione “gonfiata”


Se la porzione iniziale e’ molto piccola, la luce aveva fattoa tempo a mettere in comunicazione regioni che ora sonofuori connessione

Inoltre in questo modo la quantita’ di materia nell’Universo accessibile non dipende dalla quantita’ iniziale e tende verso il valore speciale misurato.!

La “piattezza”viene fuori naturalmente

L’ Universo puo’ naturalmente essere vicinissimo alle condizioni di perenne espansione


2001: esp. “Boomerang” per la misura di alta precisionedelle irregolarita’ del CMB

Permette di ricostruire le dimensioni angolari con cuivediamo l’epoca del disaccoppiamento

L’analisi dellevariazioni ditemperatura da’ informazionisulla proporzionedelle varie componentidell’ universo


Le misure di Boomerangsono in perfetto accordo

con la Teoria dell’Inflazione!

Lo spazio e’ piattoquindi Euclideo!

Il suo destino dipendesolo dal rapporto framateria ordinaria,

materia oscurae “energia oscura” (del vuoto)

Confermate e migliorateda WMAP


Lo stupefacente quadro della composizionedell’Universo alla luce delle misure attuali

La maggior parte dell’Universo e’ fatto di qualcosa di cuinon sappiamo nulla e che ancora non capiamo!!!


Siamo in un universo Siamo in un universo specialespeciale??

Molti indizi suggeriscono che delle condizioni dell’Universo anche solo infinitesimamente differenti avrebbero dato luogo ad un modo inospitale...L’espansione avrebbe potuto essere cosi’ veloce da non consentire la formazione di strutture.

Un’espansione appena piu’ veloce non avrebbe permesso altri atomi oltre l’idrogenoUna forza gravitazionale appena piu’ forte (o debole) avrebbe generato stelle totalmente diverse.Una forze elettro-magnetica appena diversa avrebbe prodotto atomi troppo piccoli o troppo grandi...


2 risposte possibili: 2 risposte possibili: 1) La “Teoria del Tutto”1) La “Teoria del Tutto”

2) il Principo Antropico

Una (futura) teoria della fisica spiega tutti gli aspettidell’Universo, include queste che sembrano coincidenzePuo’ esistere la Teoria di Ogni Cosa? (TOC)

a) Se l’Universo non fosse cosi’ noi non ci saremmo...

b) L’Universo e’ stato fatto per noi...c) ...esistono INFINITI UNIVERSI, con leggi

fisiche diverse. Solo in quella (infinitesima) parte di Universi in cui le condizioni lo consentono, la “vita” e’ possibile... il Multiverso


Verso una teoria super-unificataVerso una teoria super-unificataCertamente la fisica si muove in questa direzione

Progressi recenti: la teoria delle stringhe a molte dimensioni

E’ possibile arrivare ad una descrizioneunificata delle forze in uno spazio a 11 dimensioni:

Il nostro spazio-tempo a 4 dimensioni e’ una membranadi questo spazio piu’ ampio

Le altre dimensioni non sono facilmente osservabiliperche’ “arrotolate” su loro stesse:

Ma sono possibili segnali da futuri esperimenti su acceleratori


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E. Fiandrini 1 Cenni di Cosmologia Cose la cosmologia scientifica Breve storia della nostra...

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