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Home , Gravitational redshift

The expanding

Lecture 1 The early universe chapters 5to85 to 8 Particle Astrophysics , D. Perkins, 2nd edition, Oxford

5. The expanding universe 6. Nucleosynthesis and baryogenesis 7. and dark components 8. Development of structure in early universe Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmological principle, geometry of universe • part 2 : ΛCDM model ingredients: of expansion, energy density components in universe • Part 3 : observation data – , SN Ia, CMB, LSS, light element abundances - ΛCDM parameter fits • Part 4: radiation density, CMB • Part 5: Particle in the early universe, neutrino density • Part 6: matter-radiation decoupling • Part 7: Nucleosynthesis • Part 8: Matter and antimatter

2011-12 Expanding Universe 3 The ΛCDM cosmological model • Concordance model of cosmology – in agreement with all observations = Standard Model of Big Bang cosmology • ingredients: 9 Universe = homogeneous and isotropic on large scales 9 Universe is expanding with time dependent rate 9 Started from hot Big Bang, followed by short period 9 Is essentially flat over large distances 9 Made up of bar yon s, col d dark matter aadacostatnd a constant + small amount of and neutrinos 9 Is presently accelerating

2012-13 Expanding Universe 4 2012-13 Expanding Universe 5 © Rubakov 2012-13 Expanding Universe 6 Part 1 ΛCDM ingredients

Hubble expansion – Cosmological principle Geometry of the universe – Robertson-Walker metric Some distances • Earth-Sun = AU = 150 x 109 m = 150 x M km • Lightyear = Ly = 0.946 x 1016 m • 1 year = 31.5 106 s • parsec = pc = 3.3 Ly • Mpc = 3.3 MLy ruler in cosmology • Radius 15 kpc ª is~ O(Mpc) • Sun to centre MW ª 8 kpc • AdAndromed agalaxy (M31) t o earth ª 800 kpc • Width Local Group of ª 30 galaxies ª 2 Mpc • Average inter-galactic distance ª Mpc • highest redshift observed : dwarf galaxy at z ª 11

2012-13 Expanding Universe 8 Hubble law 1 • Hubble(1929): spectral lines of distant galaxies are redshifted fi galaxies move away from Earth • Receding velocity increases with distance : Amount of shift Dl depends on apparent brightness ((distance~distance D) of galaxy Original Hubble plot

SuperNovae /s)

mm Ia and II locity (k ee V

Cepeids

Distance (Mpc) 2012-13 Expanding Universe 9 Hubble law 2 • Interpret redshift z as • For relativistic objects Δλ z = λλobs− em 1+ β 1 λ ==⎯⎯⎯ obs em→+ em ( 1 ) λβem 1− λλ λ β • For close-by objects, in non-relativistic limit β λ v 11+=zzobs ≈+ββ →≈ = λem c • Hubble law becomes linear relation between velocity and Distance z c ≈ v = HD0

• Confirms theories of Friedmann and Lemaître

2012-13 Expanding Universe 10 Hubble law 3

• H0 = Hubble constant today – present value (PDG 2012)

H00==±Ht() (70.2 1.4) (km/sec) /Mp c t0 = today

HkmMpchh0 =→=±100 / sec/i 0.702 0.014 • If H(t) is same at all times → constttant and uniform expansion • Observations show that expansion was not constant and that Hubble ‘constant’ depends on time • Expansion rate evolves as function of changing energy- matter density of universe (see Friedman equations) ρ 2 2 8πG kc N t ot Ht()=−()t 2 3 (Rt( ))

2012-13 Expanding Universe 11 Sources of redshift • Motion of object with respect to observer – Doppler effect (red and blue shifts): e.g. rotation of stars in galaxies – see galaxy rotation curves (dark matter) • Gravitational redshift :stretchingof: stretching of wavelength close to heavy object - local effect – negligible over long distances • Cosmological redshift :stretchingof: stretching of wavelength due to expansion of universe – dominant at high redshifts

λobs ()tRt00() 1+=z = R(t)=Scale of universe at time t λem (tRt) ( )

2012-13 Expanding Universe 12 Cosmological redshift - time • Redshift is the measured quantity – it is related to a given time during the expansion • Large z means small t , or early during the expansion t 0 tt= Big = 0 today Bang z =∞ z = 0

• Actual (proper) distance D from Earth to distant galaxy at time t Dt()=⋅ rR t () • D can ooynly be measur ed for near by objects • r = co-moving coordinate distance – in reference frame co- moving with expansion - in which 2 objects are at rest

2012-13 Expanding Universe 13 Cosmological principle - large scales • universe is isotropic and homogeneous at large scales • There is no preferred position or direction • Expansion is identical for all observers • Is true at scale of inter-galactic distances : O(Mpc)

•2dF survey •Two slices in Ri

declination and right g ascention asce ht •Plot redshift vs right n ascension sion •Each dot = galaxy

2012-13 Expanding Universe 14 Cosmic Microwave Background photons

WMAP 5 years data Uniform temperature up to ΔT/T ~ 10-5

2012-13 Expanding Universe 15 Structures - small scales • Over short distances universe is clumpy • Galaxy clusters O(10 Mpc) diameter • galaxies, eg Milky Way : 15 kpc COMA cluster: 1000 galaxies 20Mpc diameter M74- IR 100 Mpc(330 Mly) from Earth Optical + IR

Milky Way 2012-13COBE - radio Expanding Universe 16 Olbers’ paradox • Olber (~1800): Why is the sky not bright at night? • Suppose that universe is unlimited & filled uniformly with

light sources (stars) - total flux expected is μ rmax ¾ The sky does not look dark because: • has finite age – for constant

expansilihtion: light can reach us from maximum rmax = O(c t0 ) • Stars emit light during finite time Dt – flux reduced by factor Dt/t0 • Light is redshifted due to expansion - eg red light Æ IR – finally undetectable flows • CMB fills universe – dark matter does not liggpht up

2012-13 Expanding Universe 17 Robertson-Walker metric 1 ¾ assume universe = homogeneous and isotrope fluid • Distance between 2 ‘events’ in 4-dimensional space-time

ds222 c dt⎡ dx 2 dy 2 dz 2⎤ Co-moving =−++⎣⎦distance dr ¾ Universe is expanding • scale factor R(t), identical at all locations, only dependent R t on time 2222 2 2 2 ds=− c dt( (( )) ) ⎣⎦⎡⎤ dx ++ dy dz

• proper distance D from Earth to distant galaxy at time t Dt()=⋅ rR t () • r = co-moving coordinate distance

2012-13 Expanding Universe 18 Stretching of the universe scale Example: closed universe

R(t ) R(t1) 2

© LBL. Bergs tötröm

2012-13 Expanding Universe 19 Robertson-Walker metric 2 ¾ space is not necessarily flat • Introduce k = spatial curvature of universe • Distance between 2 events in 4-dim space-time

R2 2 222t ⎡⎤dr 2 2 2 2 ds=− c dt()⎢ 2 + r() dθθφ +sin d ⎥ ⎣⎦1− kr

• k:k : curvature of space → geometry – obtained from observations – can be -1,0,1 • R(t) : dynamics of expansion → Friedman-Lemaître equations – model dependent

2012-13 Expanding Universe 20 Curvature k in FLRW model • k = +1, 0, -1 depends on space geometry • Curvature is independent of time • Curvature is related to global -energy density of universe kc2 Ω−=()t 1 energy− matter HtRt22() () • It affects the evolution of density fluctuations in CMB radiation – path of is different • Therefore it affects pattern of the CMB radiation today • For universe as a whole, over large distances, space-time seems to be flat: k=0 from CMB observations

ρρtot (tt)= crit ( )

2012-13 Expanding Universe 21 Global energy CiCosmic dtidestiny geometry density

k<0 expands for ever

k=0 velocity asymptotically zero

k>0 big crunch

2012-13 Expanding Universe 22 Excercise • D. Perkins, chapter 5 • Oplossing meebrengen op het examen

2012-13 Expanding Universe 23 k from CMB observations

movie Curvature of universe CMB photons z = 1100 t=380.000 y model

k0k<0 k>0 z = 0 observe

k=0

2012-13 Expanding Universe 24 Hubble time – Hubble distance • Expansion parameter H(t) has dimension of (time)-1 • Hubble time = expansion time today for constant expansion

11 9 tt= ⇒ 0 ==×13.9 10 year Ht() H0 • Horizon distance today in flat static universe (Hubble

distance) DtH ()00== ct4.2 Gpc

• But! Look back time and distance in expanding universe depend on dyn ami cs in H(t) (see par t 2 ) 2 2 8πG ρ kc N t ot Ht()=−()t 2 3 (Rt( ))

2012-13 Expanding Universe 25 Matter dominated flat universe • Integration of Friedman equation with k=0 and only non- relativistic matter 1 3 2 ⎛⎞9GM 3 R(tt)= ⎜⎟ ⎝⎠2 21 1 Rt( 0 ) 3t0 9 == tyr0 ==×919.110 10 3 H HRt00()2 0

• Dating of earth crust and old stars shows that age of uueseniverse is of ooderder 14 x 109 yr • → Need other energy components (see part 2)

2012-13 Expanding Universe 26 Part 2 ΛCDM ingredients

Dyypnamics of the expansion – Friedman Lemaître equations Energy density of universe Dynamics of the expansion • of 1 RGTRg− ℜΛℜ =−8π GTgΛ νμ νμν μν μν μν 2 N

⎛⎞μν Λgμν Cosmological =−8πGTN ⎜⎟constant ⎝⎠8 GN Geometry of space-time Energy-momentumπ Robertson-Walker metric Function of energy content of universe

−11 3 -1 -2 Is model dependent GN =×6.67 10 m kg s • Friedmann & Lemaître (1922) : Solutions for uniform and homogeneous universe behaving as perfect frictionless fluid

2012-13 Expanding Universe 28 Friedmann-Lemaître equation • Time dependent evolution of universe = Friedman-Lemaître 2 equation 2 2 ⎛⎞Rt( ) 8πG ρ kc H t ≡ =−N t ot t ( ) ⎜⎟ ( ) 2 ⎝⎠Rt() 3 ()R()t kc2 R2= curvature term ρ t ot ()t = energy density of universe globally, 'at large'

Ht( )= expansion rate = Hubble 'constant' at ti me t H H t = 70.2 1.4km /Mpc = Hubble constant today 0 =±()(0 ( )s ) • energy density ρ is model dependent - ΛCDM model :

ρtot (tt)=+ρρbaryon( ) coldDM( tt) ++ ρρ rad( ) DarkEn

2012-13 Expanding Universe 29 Second Friedman equation • Consider universe = perfect fluid with energy density ρc2 • Conservation of energy in volume element dV ; P = pressure of fluid

23 3 ⎛⎞R dE=− PdV dcRρ ⋅=− PdR 2 ()()ρρ=−3()Pc + ⎜⎟2 ⎝⎠Rc

• Differentiate 1st Friedman equation3& substitute ρ + P dR ⎛⎞4πGRN ⎛⎞ R ==−⎜⎟⎜⎟c2 Equation of state dt ⎝⎠3 ⎝⎠ • ΛCDM model : Energy density consists of 3 components: matter, radiation (incl. relativistic particles), constant vacuum energy Λ ρ =+ρρmatterradiation ρ + vacuum ρ with ρ vac ==Λ 8πGN

2012-13 Expanding Universe 30 Equations of state 1 1. Matter component: ‘dust’ of non-relativistic particles (v<

gravitational repulsion 2 Pvac =−ρccst =

2012-13 Expanding Universe 31 Equation of state 2 • Relation between pressure and energy - introduce w P = w ρc2 ⎛⎞R ⎛⎞R 2 2 ρ =−3(P +ρc )⎜⎟2 ρ =−31ρcw() + ⎜⎟2 ⎝⎠Rc ⎝⎠Rc

−+31()w 31+w ρ =∝+const R()1 z () 2 β R ~ t 31+w • For small t assume that Rt∼ t() 1 () radiati on w 1 2 = 3 R ∼ t 2 matter w = 0 R ∼ t 3 vacuum w1& const =−ρ = R ∼ eHt 2012-13 Expanding Universe 32 31+w ρ ∝ (1+ z) ( )

wDarkEnergy =−10210± .2 © J. Frieman

2012-13 Expanding Universe 33 Critical density • flat universe (k=0) = equilibrium between open and close universe • Friedmann equation becomes ⎛⎞Rt 2 8πρ G ρ 3H 2 Ht2 ≡=() c N ⇒ c= ()⎜⎟2 ⎝⎠Rt( ) 38π GN

• density ρc is called critical density • Value today is 2 3H0 −−27 3 ρc ()tkgm0 ==×9.6 10 8πGN 23 3 ρccGeVm=≈5.4 5 protons at rest per m

• Observations →universe is geometrically flat, so present average density of universe, away from galaxies, is a few protons per m3

2012-13 Expanding Universe 34 closure parameter • Define closure parameter W Ω t ρ t () ()= ρc (t)

• For general geometry with k≠0, Friedmann equation becomes 222 8πG H 2 ⎛⎞Hkc N = ⇒ H =−⎜⎟ 3 ρρ1 = R2 cc⎝⎠Ω t - kc2 ρ ()t kc2 1 =− ⇒ H2 22 ( ) t ρ (tHR) ρ ( ) R2( ) c t • Define curvature term Observations: Ω 2 flat universe k ρK kc ==− Ω+Ω=()ttk ()1 and Ω=1 at ρ H 22R c all times

2012-13 Expanding Universe 35 pauze

2012-13 Expanding Universe 36 Observed energy densities 1 • Energy density is composed of: dust/matter (non-rel), radiation (incl. rel particles), vacuum energy (L) Ω Ω+Ω =()m + Ω +Ω =1 kkr + Ω • Relative contributions unfluence dynamicsΛ of expansion ¾ Present-day observations: 1. Radiation (from CMB energy density) ρ (t ) rad 0 −5 Ωrad (t0 )=≈×510 ρc ()t0 2. Luminous baryonic matter : p, n, nuclei in stars, gas, dust

−−29 3 ρlum ρlum≈×9 10kg m ⇒ Ω= lum ≈ 0.01 ρc

2012-13 Expanding Universe 37 Observed energy densities 2 3. total baryon density – from fit of the model of primordial nucleosynthesis to measurements of light element abundances (chapter 6) −3 nmb ≈ 0.26 baryons −−28 3 ρbb=×4.0 10kg m ⇒ Ω= 0.042 ± 0.004 4. TtlTotal matter ditdensity-from galtilacticrottitation curves, gravitational lensing, etc (chapter 7) - is clumpy in ΛCDM model this is composed of baryons and (mostly cold) dark matter −−27 3 ρmm=×2.2 10kg m ⇒ Ω=Ω+Ω=BDM 0.24 ± 0.03 5. Neutrino density – relics of early universe Ω<ν 0. 004− 0.02

2012-13 Expanding Universe 38 Observed energy densities 3 5. total density: fit of ΛCDM cosmological model to large set of observation data (CMB, SN, …) – PDG 2010

Ω=−Ω=±total 1k 1.006 0.006 k ≈ 0 6. By subtraction we obtain the vacuum energy density non clumpy – homogeneous effect – PDG 2010

Ω=Λ 0.726 ± 0.015 ¾ Conclusions: – 95% of energy content of universe is of unknown type – Today most of it is dark vacuum energy – See further in chapter 7

2012-13 Expanding Universe 39 Evolution of energy components 1 • Cosmological redshift is related to the expansion rate R t ( 0 ) 31( +w) 10+=zzt( 0 ) = 1 z Rt() ρ ∝+( ) 1. RditiRadiation = p hthotons an d reltiitilativisticpartic les

22Ehν 11 1 ρρcc= ∼∼⇒ ( ) ∼ VR33λ Rrad R 4 24 ρct() Rt ( ) 44 ==+0 11zcz⇒ ρ 2 ∼ + 24( ) ( )rad ( ) ρct()0 Rt() 2. Non-relativ istic matter

22Em 113 ρρccz= ∼∼⇒ ( ) ∼∼(1+ ) VR33 Rm R 3

2012-13 Expanding Universe 40 Evolution of energy components 2

3. Vacuum energy is constant in our model ρccst2 = ()Λ 4. Curvature term

2 22−kc 1 2 ρρccz= ⇒ ( ) ∼∼(1+ ) HR22k R 2

• Dynamics of expansion can be rewritten 8πG H 2 (ttttt)=+++⎡⎤ρ ( ) ρρ( ) ( ) ρ( ) 3 ⎣⎦mrΛ k 2 ⎡⎤ = Htt0 ⎣⎦Ω+Ω+Ω+Ωmr( ) ( ) Λ ( tt) k ( ) Hz2 ⎡⎤t 113 t z 42tt 1z =++++0 ⎣Ωmr()00()ΩΩ()()Λ 0 ++Ωk 0()⎦ ()()

2012-13 Expanding Universe 41 Summary

4 radiationρ c2 ∼ (1+ z) 3 matterρ c2 ∼ ()1+ z vacuumρ c2 ∼ cst 2 curvatureρ c2 ∼ ()1+ z

2012-13 Expanding Universe 42 Lookback time

11dR dR ()1+ z dR H = ⇒ dt == Rdt RHHR( t) dz 0 dt =− ⎡ 1 z H ⎤ Rt()0 −1 ⎣()+ ⎦ Rt( )= ⇒ dR = Rt( 0 ) 2 dz 1+ z ()1+ z

• Time elapsed between emission of a photon at expansion

time tE by object at redshift zE and today t 0 0 dz tt0 −=E dt =− ∫∫⎡⎤1+ z Hz tE zE ⎣()()⎦

2012-13 Expanding Universe 43 • Age of universe from integration

From Big Bang time ( t=0 and z=∞) to present time ( t=t0 and z=0) t 0 0 dz tdt0 0 − ==∫∫− 0 ∞ ⎣⎡()()1+ z Ht⎦⎤

• Example:flat: flat universe (Wk=0) with Wm=0.24, WΛ=0.76

t0 = (13. 95± 0. 4)Gyr

• Uitwerking meebrengen op examen

2012-13 Expanding Universe 44 Age of the universe

()Ω+Ω+Ω+Ω=mrΛ k 1

Ω r = 0 Ω k = 0 Ω =m 0.24 Ω Ht00 m Λ =−1Ω = 0.76

Ht00=1.026

tG0 =±(13.95 0.4) yr

Only matter

2012-13 Ωm Expanding Universe 45 Horizon 1 • Extent of region accessible via light signals to comoving observer at given time t static− flat • In static flat universe DtctGpcH ()00==4.2 • In an expanding FLRW universe, for a photon following a line with fixed θ and φ = ⎡⎤dr 2 2 cRt22dt 2 ds = 0 ( )⎢ 2 ⎥ ⎣1− kr ⎦

• Proper distance travelled by photon emitted at time tE and comoving position r E Dt( 00)=⋅ rE Rt( )

• Observed at time t0 and position r=0

2012-13 Expanding Universe 46 Horizon 2

• Particle horizon for observer at time t0 : tE →0

⎡⎤rE dddr t0 cdt DH ()tRtRt000==i () () ⎢⎥∫∫002 ⎣⎦1− kr R t ()

• Expanding, flat, radiation dominated universe 1 Rt() ⎛⎞t 2 = ⎜⎟ DtH ()00= 2 ct Rt( 00) ⎝⎠ t • Expanding, flat, matter dominated universe

2 3 Rt() ⎛⎞t Dt()= 3 ct = ⎜⎟ H 00 Rt( 00) ⎝⎠ t

2012-13 Expanding Universe 47 Horizon 3 • For a more complex cosmological model

r dr cdz cI( z) Rt() =− = 0 ∫∫2 0 1− kr HH0 z dz Iz ()= ∫ 1 34 22 0 ⎡⎤Ω++Ω++Ω+Ω+ttt 11z t z tt 1z ⎣ mr( 00)( ) ( )( ) Λ ( 00) K( )( ) ⎦

• For Wk=0, Wm=0.24, WΛ=0.76 and integration to z=∞

BBexpansion c DctGpcH ∼∼3.3= 3.30 14 H0

2012-13 Expanding Universe 48 Deceleration parameter 1

• Taylor expansion of expansion parameter around t0 (present time)

⎛⎞1 2 Rt()=+ Rt000 ( Rt ) t ( −+ t )(⎜⎟ Rt )()( 00 t −+ t ) ⎝⎠2 R t0 Rt() ⎛⎞1 ⎡⎤()R ()2 2 2 t0 =+1 H (ttt00)( −)− ⎢⎥− R Httt( 00)( −) + ⎜⎟ t0 R(t0 ) ⎝⎠2 ⎣⎦⎢ ( ) ⎥

Rt 1 q 2 ( ) ⎛⎞ 0 2 =1+++ Htt00( −−)− ⎜⎟ Htt 0( 0) + Rt()0 ⎝⎠2

• Deceleration parameter q(t): acceleration or deceleration of expansion at time t

2012-13 Expanding Universe 49 Deceleration parameter 2 • Deceleration parameter q(t) is related to energy density at time t – for flat universe (k=0) 2 RR⎛⎞ R ⎛⎞ R qt =− =− () 2 ⎜⎟⎜⎟ q() t> 00⇒ R< ⇒ deceleration RRR⎝⎠⎝⎠ q() t< 00⇒ R > ⇒ acceleration ⎡ 41πG 2 ⎤⎛ ⎞ qt()=− −22( c +3 P) ⎜⎟ ⎣⎦⎝⎠⎢⎥3cHρ • Energy-pressure relation: equations of state for –Dust/matter – Radiation/relativistic particles – Vacuum energy Ωm t () qt()=+Ω−Ω() t t () 2 r Λ

2012-13 Expanding Universe 50 Acceleration or deceleration?

Ωm t () qt()=+Ω−Ω() t t () 2 r Λ • A universe dominated by matter decelerates due to gravitational collapse : qt()∼ Ω>m t ()00⇒ R<

• A universe dominated by vacuum energy accelerates qt( )≈−ΩΛ ( t) <00⇒ R> • Observations show that today

ΩΩrm⎫ ⎬ ⇒ qt()00< 00⇒ Rt > () Ω>ΩΛ m ⎭

2012-13 Expanding Universe 51 Deceleration in past & accelerationPhysics Nobel prize 2011 now

2012-13 Expanding Universe 52 Part 3 Observation data Redshift measurements Luminosity distance SNSuperNovae Ia Cosmic Microwave Background Large galaxy surveys Light element abundances Measuring redshift • Atoms emit light at certain wavelengths – is measured 2000 4000 6000 in laboratory (atom at rest) Restframe wavelength (Å) • Atoms in emit same spectrum but light is CIV redshifted when reaching Earth • Comparison of observed spectrum with lab spectrum gives redshift z

2012-13 Expanding Universe 54 examples

λ ()t 1+=z obs 0 λem (t)

2012-13 Expanding Universe 55 Magnitude and distance

• Luminosity distance DL to star with intrinsic luminosity L • F = power measured at Earth L F = 2 4π DL • Absolute magnitude M = magnitude at 10pc distance • Effective magnitude m of star with absolute magnitude M M =−2.5log Lcst +

⎛⎞DL m ()zM−=5log10 ⎜⎟ + 25 ⎝⎠1Mpc

• Large negative magnitude = bright star: e.g. m(()Sun)=-26 ;;( m(, brightest star) = -1.7 • Far away object is dimmer and has larger (=smaller negative) m

2012-13 Expanding Universe 56 SN Ia as standard candles • Supernovae Iaare verybihtbright – lig ht from very dis tan t SN can be observed – up to z=1.7 • Are poor • All have roughly the same luminosity curve

M101 at 20 Mly SN2011fe Flashed on 18 december 2011

2012-13 Expanding Universe 57 SN Ia as standard candles • 1995 ( Hamuy, Philips ): re la tion btbetween peak liitluminosityand dlidecline rate ee agnitud mm olute ss Ab

Δm15

2012-13 Expanding Universe 58 SN Ia – Nobel Prize 2011 • S. Perlmutter - Supernova Cosmology Project (SCP) http://supernova.lbl.gov/ • A. Riess & B. Schmidt – High-z Supernova Search Team (HZSNS) http://www.cfa.harvard.edu/supernova//HighZ.html • High statistics SN monitoring 18 December 1998 – Distance: observed magnitude + absolute magnitude from lightcurve – Redshift from spectra Breakhkthrough ofhf the year • 1998: discover accelerated cosmic expansion

2012-13 Expanding Universe 59 Deceleration in past & accelerationPerlmutter, now 2003

0% matter

100% matter

Lage dichtheid Versnelde expansie

e D(z) grote dic hthe id Vertraagde expansie istanc d now Redshift z past

2012-13 Expanding UniverseR()zRt==10.5 × 0 60 () CMB in Big Bang model • early hot universe : radiat ion (reliiilativisticpartilicles) didominates over matter (dust, non-relativistic particles) & vacuum energy is negligible • When cooled down below kT ª few MeV : – Free p, n, e, g (+neutrino’s) – Plasma o f H+ andHd He++ nuclilei − – Matter-radiation thermal equilibrium epH+↔ +γ • When EV(iitiE < eV (ionisation pottiltentials) : recombina tion to atoms epH− +→ +γ 1z 1100 and ty 380.000 and T 3000 K ()+≈dec dec ≈dec ≈ • Matter-radiation decoupling • Expect to see γ’s today as uniform Cosmic Microwave Background • Observed 3K background photon radiation with black body spectrum

2012-13 Expanding Universe 61 Structure AiAniso trop ies in formation in atom distribution early universe? are ‘frozen’ in CMB

CMB photons are released

© Univ Oregon

2012-13 Expanding Universe 62 What can we learn from CMB • Density (pressure) anisotropies in photon-baryon fluid at time of decoupling should leave imprint in distribution of g’s today • observe temperature anisotropies O(10-5)

• Growth of anisotropies depends on dark matter & dark energy during expansion • Angular distance between 2 photon directions depends on curvature of space

• CMB observations probe universe at z ~1100

2012-13 Expanding Universe 63 Large Scale Structures • Redshift measurements of large samples of galaxies • (SDSS 2000-2014): million of galaxies being recorded • On average uniform population • Galaxies = baryonic matter • Density (pressure) anisotropies in photon-baryon fluid at time of decoupling are expected to leave imprint in distribution of baryons today • Baryon Acoustic Oscillations (BAO) observations probe universe at small z – are sensitive to dark matter

2012-13 Expanding Universe 64 2dF quasar redshift survey 2003

SDSS survey of local sky Low z – recent universe Baryon Acoustic Oscillations

2012-13 Expanding Universe 65 Abundances of light elements • Model of predicts abundances of light nuclei: H, D, He, Li , .. • They were formed at t ~3min when kT ~ 3MeV • Abundances are measured today – probe expansion model before decoupling

• Allow to measure baryon ditdensity Ω±Ωb = 0. 042± 0. 004

2012-13 Expanding Universe 66 Pdg.lbl.gov Fit ΛCDM model to observations

SN Ia distance-redshift surveys Ω Λ

CMB anisitropies survey by WMAP Anisotropies in galaxy surveys Ω m 2012-13 Expanding Universe 67 Fit ΛCDM model to observations Pdggg.lbl.gov

2012-13 Expanding Universe 68 Expanding universe : content • part 1 : ΛCDM model ingredients: Hubble flow, cosmological principle, geometry of universe • part 2 : ΛCDM model ingredients: dynamics of expansion, energy density components in universe • Part 3 : observation data – redshifts, SN Ia, CMB, LSS, light element abundances - ΛCDM parameter fits • Part 4: radiation density, CMB • Part 5: Particle physics in the early universe, neutrino density • Part 6: matter-radiation decoupling • Part 7: Big Bang Nucleosynthesis • Part 8: Matter and antimatter

2011-12 Expanding Universe 69