The expanding universe

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

5. The expanding universe 6. Nucleosynthesis and baryogenesis 7. and dark energy 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: 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 • Part 7: Nucleosynthesis • Part 8: Matter and antimatter

2013‐14 Expanding Universe lect1 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 baryo ns, col d dark matter aadnd a con stant dark energy + small amount of and neutrinos 9 Dark energy is related to cosmological constant Λ

2013‐14 Expanding Universe lect1 4 2013‐14 Expanding Universe lect1 5 Lecture 3

Lecture 1 2

e rr Lectu

Lecture 3

Lecture 4 © Rubakov 2013‐14 Expanding Universe lect1 6 Part 1 ΛCDM ingredients

Hubble expansion – redshift 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 • = pc = 3.3 Ly • Mpc = 3.3 MLy ruler in cosmology • Radius Milky Way 15 kpc ª is~ O(Mpc) • Sun to centre MW ª 8 kpc • AdAndromed agalaxy (M31) to 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

2013‐14 Expanding Universe lect1 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) 2013‐14 Expanding Universe lect1 9 Hubble law 2 • Interpret redshift z as Doppler effect • 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

2013‐14 Expanding Universe lect1 10 Hubble law 3

• H0 = Hubble constant today – best direct estimate (HST, WFC3) HHt00==±( )( 73.8 2.4) (km/sec) /Mpc t0 = today HkmMpchh0 =→=±100 / sec/i 0.738 0.024 • If H(t) is same at all times → constant and uniform expansion • Observa tions show tha t expansion was not constttant 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( ))

2013‐14 Expanding Universe lect1 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 : stretching of wavelength close to heavy object ‐ local effect – negligible over long distances • Cosmological redshift : 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) ( ) Also called a(t)

2013‐14 Expanding Universe lect1 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

2013‐14 Expanding Universe lect1 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 quasar survey •Two slices in Ri

declination and right g ht

ascention •Plot redshift vs right asce n ascension sion •Each dot = galaxy

2013‐14 Expanding Universe lect1 14 Equatorial coordinates

2013‐14 Expanding Universe lect1 15 Cosmic Microwave Background photons

WMAP 5 years data ‐ 2.75°K sky Uniform temperature up to ΔT/T ~ 10‐5

2013‐14 Expanding Universe lect1 16 Cosmic Microwave Background photons PLANCK 4 years of data – 2.75°K sky Uniform temperature up to ΔT/T ~ 10‐5

© NASA, ESA

2013‐14 Expanding Universe lect1 17 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 2013COBE‐14 ‐ radio Expanding Universe lect1 18 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 ~ rmax ¾ The sky does not look dark because: • has finite age – for constant

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

2013‐14 Expanding Universe lect1 19 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 • 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

2013‐14 Expanding Universe lect1 20 Stretching of the universe scale Example: closed universe

R(t ) R(t1) 2

© L. BtöBergström

2013‐14 Expanding Universe lect1 21 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 : curvature of space → geometry – obtained from observations –canbe‐1,0,1 • R(t) : dynamics of expansion → Friedman‐Lemaître equations – model dependent

2013‐14 Expanding Universe lect1 22 Curvature k in FLRW model • k = +1, 0, ‐1 depends on space geometry • Curvature is independent of time • Curvature is related to total mass‐energy density of universe kc2 Ω ()t −=1 total HtRt22() () • It affects the evolution of density fluctuations in CMB radiation –pathof 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 ( )

2013‐14 Expanding Universe lect1 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

2013‐14 Expanding Universe lect1 24 Global energy CiCosmic dtidestiny geometry density

k<0 expands for ever

k=0 velocity asymptotically zero

k>0 big crunch

2013‐14 Expanding Universe lect1 25 Excercise • D. Perkins, chapter 5 • Oplossing meebrengen op het examen

2013‐14 Expanding Universe lect1 26 Hubble time – Hubble distance • Expansion parameter H(t) has dimension of (time)‐1 • Hubble time = expansion time today for constant expansion

1 9 t0 ==×13.6 10 year H0 • Hubble distance = Horizon distance today in flat static

universe DtH ( 00)= ct= 4.2 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( ))

2013‐14 Expanding Universe lect1 27 Example: 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 ooderder14 x 109 yr • → Need other energy components (see part 2)

2013‐14 Expanding Universe lect1 28 Part 2 ΛCDM ingredients

Dynamics of the expansion – Friedman Lemaître equations Energy density of universe Dynamics of the expansion • Einstein field equations 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

2013‐14 Expanding Universe lect1 30 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 = 73.8 2.4km /Mpc = Hubble constant today 0 ()(0 ( s )) • energy density ρ is model dependent - ΛCDM model :

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

2013‐14 Expanding Universe lect1 31 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 dcR(ρ ⋅=−) 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

2013‐14 Expanding Universe lect1 32 Equations of state 1 1. Matter component: ‘dust’ of non‐relativistic particles (v<

gravitational repulsion 2 Pvac =−ρccst =

2013‐14 Expanding Universe lect1 33 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 w=−1&ρ = const R ∼ eHt 2013‐14 Expanding Universe lect1 34 31+w ρ ∝+(1+ z) ( )

wDarkEnergy =−10210 ± .2 © J. Frieman

2013‐14 Expanding Universe lect1 35 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

2013‐14 Expanding Universe lect1 36 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(tt)()+Ωk =1 and Ω=1 at ρ H 22R c all times

2013‐14 Expanding Universe lect1 37 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

ρlum Ω=lum <0.01 ρc

2013‐14 Expanding Universe lect1 38 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≈ 0.04 4. TtlTotal matter ditdensity – from fit to CMB ddtata ‐ isclumpy in ΛCDM model this is composed of baryons and (mostly cold) dark matter

Ωm =Ωb +ΩDM =0.31 5. Neutrino density – relics of early universe – from fit to

CMB data Ω≤ν 0010.01

2013‐14 Expanding Universe lect1 39 Observed energy densities 3 5. total density: fit of ΛCDM cosmological model to large set of observation data (CMB, SN, …) – PDG 2013

Ωtotal =−Ω=1k 1.0005 ± 0.0033 k ≈ 0 6. By subtraction we obtain the vacuum energy density non clumpy – homogeneous effect – PDG 2013

ΩΛ =±0.692 0.010 ¾ Conclusions: – 95% of energy content of universe is of unknown type – Today most of it is dark vacuum energy Ω ≈ 0310.31 – See further in chapter 7 m Ω≈Λ 0.69

2013‐14 Expanding Universe lect1 40 Evolution of energy components 1 • Cosmological redshift is related to the expansion rate R(t ) 10+ zzt==0 ( ) 31( +w) Rt() 0 ρ ∝+(1 z) 1. RditiRadiation = phhtotons and reltiitilativisticpartic les Ehν 11 1 ρρcc22= ∼∼⇒ ( ) ∼ VR33λ Rrad R 4 24 ρct() Rt0 ( ) 44 ==+⇒(11zcz) (ρ 2 ) ∼ ( +) 24 rad ρct( 0 ) Rt( ) 2. Non‐relativ istic matter – clmplumpy matter Em 113 ρρccz22=⇒∼∼⇒+( ) ∼∼(1 +) VR33 Rm R 3

2013‐14 Expanding Universe lect1 41 Evolution of energy components 2 3. Vacuum energy is constant in our model ρccst2 = ( )Λ 4. Curvature term

2 −kc 1 2 ρρccz22=⇒( ) ∼∼(1 +) HR22k R 2

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

2013‐14 Expanding Universe lect1 42 Summary

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

2013‐14 Expanding Universe lect1 43 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 ⎣ ⎦

2013‐14 Expanding Universe lect1 44 • 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 tdt−=0 == =− 0 ∫∫ 0 ∞ ⎣⎡(1+ z)Ht( )⎦⎤

• Example: flat universe (Wk=0) with Wm=0.24, WΛ=0.76 (WMAP results) tGyr0 =±(13.95 0.4)

• Uitwerking meebrengen op examen

2013‐14 Expanding Universe lect1 45 Age of the universe

()Ωmr+Ω +ΩΛ +Ωk =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

2013‐14 Ωm Expanding Universe lect1 46 Particle horizon 1 • Maximum distance accessible via light signals to an

observer at given time t0 ? 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

2013‐14 Expanding Universe lect1 47 Particle 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

2013‐14 Expanding Universe lect1 48 Particle horizon 3 • For a more complex cosmological model

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

2013‐14 Expanding Universe lect1 49 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

2013‐14 Expanding Universe lect1 50 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

2013‐14 Expanding Universe lect1 51 Acceleration or deceleration? Ω (t) qt()=+Ω−Ωm () t t () 2 r Λ • A universe dominated by matter decelerates due to gravitational collapse : qt( )()∼ Ωm t>⇒<00 R

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

ΩΩ rm⎫ ⎬ ⇒<⇒>qt()0000 Rt () Ω>ΩΛ m ⎭

2013‐14 Expanding Universe lect1 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 quasars emit same spectrum but light is CIV redshifted when reaching Earth • Comparison of observed spectrum with lab spectrum gives redshift z

2013‐14 Expanding Universe lect1 54 examples

λ (t ) 1+=z obs 0 λem (t)

2013‐14 Expanding Universe lect1 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((,Sirius, brightest star) = ‐1.7 • Far away object is dimmer and has larger (=smaller negative) m

2013‐14 Expanding Universe lect1 56 SN Ia as standard candles • Supernovae Iaare very bihtbright – lig ht from very dis tan t SN can be observed – up to z=1.7 • Are hydrogen poor • All have roughly the same luminosity curve

M101 at 20 Mly SN2011fe Flashed on 18 december 2011

2013‐14 Expanding Universe lect1 57 SN Ia as standard candles • 1995 (Hamuy, Philips ): reltilation btbetween peak liitluminosityand dlidecline rate

• Measure Δm15 ‐> obtain M ee agnitud mm olute ss Ab

Δm15

2013‐14 Expanding Universe lect1 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 of the year • 1998: discover accelerated cosmic expansion • Probe history at z < 2

2013‐14 Expanding Universe lect1 59 The principle Deceleration in past & accelerationPerlmutter, now 2003

0% matter

100% matter

Low density

D(z) Accelerated expansion

e High density Decelerated expansion istanc d now Redshift z past

2013‐14 Expanding Universe lect1R(zRt==10.5)() × 0 60 Recent survey of SuperNovae

arXiv:1105.3470v1

2013‐14 Expanding Universe lect1 61 Abundances of light elements • Model of Big Bang Nucleosynthesis predicts abundances of light nuclei: H, D, He, Li , .. • They were formed at t ~20min when kT ~ KeV and z>>1100 • Abundances are measured today • probe expansion model at redshift z >> 1100, before creation of CMB • Allow to measure baryon density ΩB =±0.044 0.005

• See lecture 2

2013‐14 Expanding Universe lect1 62 Big Bang Nucleosynthesis + − • when kT ~ 3 MeV , left with e ,e ,ν ,,νμ(e, τ ) γ ,,p n, p,n • Neutrinos decouple, anti‐particles are annihilated • FtFateof bb?aryons? → Big Bang NlNucleosynth thiesismodldel • Protons and neutrons in equilibrium due to weak + − interactions ν e + p ↔+e n n →+p e +ν e • Neutrons are ‘saved’ by binding to protons → deuterons np+ ↔++ Dγ 2.22 MeV • At kT ~ 80 KeV (20 mins) np+→++ Dγ 2.22 MeV • Formation of light nuclei 234H,,3H He,.. He , • Fractions of elements predicted by BBN model

2012‐13 Expanding Universe 63 Cosmic Microwave Background • after fiformation of lig ht nuclilei (BBN modl)del) around t=20 mins • Plasma of H+, He++ , … nuclei, plus e‐ and photons –in thermal equilibrium • At recombination (380’000 y) , when E < eV (ionisation potentials) ‐ nuclei + e → atoms + CMB photons − epH+ →+γ CMB

1+≈z 1100 and ty ≈380 .000 and T30 T ≈ 3000K ( )dec dec dec

• Matter‐radiation decoupling • Expect to see γ’s today as uniform Cosmic Microwave Background • Observe d 3K bkbackground phthoton radia tion with blac k bbdody spectrum • Probe history at z = 1100

2013‐14 Expanding Universe lect1 64 Cosmic Microwave Background

Matter

photons are released

© UiUniv Oregon

Baryons/nuclei and ¾Photons decouple/freeze‐out photons in ¾During expansion they cool thermal equilibrium down ¾Expect to see today a uniform γ radiation which behaves like a black bbdody radiati on

2012‐13 Expanding Universe 65 Structure AiAniso trop ies in formation in atom distribution early universe? are ‘frozen’ in CMB

CMB photons are released

© Univ Oregon

2013‐14 Expanding Universe lect1 66 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 evolution of matter, radiation and dark energy during expansion • Angular distance between 2 photon directions depends on curvature of space

2013‐14 Expanding Universe lect1 67 Large Scale Structures • Redshift measurements of large samples of galaxies • For ex.: Sloan Digital Sky Survey (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 galaxies today • ‐> Baryon Acoustic Oscillations (BAO) observations • probe universe at z <~ 5 –or evolution during last 7Gyears

2013‐14 Expanding Universe lect1 68 2dF quasar redshift survey 2003

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

2013‐14 Expanding Universe lect1 69 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 2013‐14 Expanding Universe lect1 70 Fit ΛCDM model to observations Pdggg.lbl.gov

2013‐14 Expanding Universe lect1 71