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Home , Blueshift

Introduction to Cosmology

V.Ruhlmann-Kleider CEA/Saclay Irfu/DPhP

1) The model 2) Content of the 3) Cosmological probes 4) Beyond concordance

October 19, 2018 Sarajevo school of High- Physics 1 The rise of the Big Bang model

Orders of magnitude. The three pillars of the Big Bang model

§ Distances, cosmological scales § § Expansion of the Universe, the metric § The rise of the Big Bang model

2 1. Distances

§ solar system: Earth-Sun ~ 150. 106 km ~ 1 AU

§ , eg the : ∅ ~100,000 lyr ~ 30kpc Sun-Gal. center ~ 10kpc 1lyr=63,240 AU 1pc=3.26 lyr 1Mpc=3.3 106 lyr

§ clusters: largest and most massive gravitationally bound structures, 50 to 1,000’s of galaxies, ∅ ~ 2 to 10 Mpc

§ large scale structures: galaxies → clusters → superclusters (15 – 100Mpc) making a network of voids (25 – 125Mpc) and filaments (90 – 300 Mpc) ⇒ beyond 100Mpc, homogeneous and isotropic Universe X 6dF Galaxy Redshift Survey, (2009) 3 2. Redshift

§ Emitted spectrum ⇒ spectral lines ⇒ astro. object composition, environment … and motion relative to Earth.

§ Redshift : the object moves away from us ⇒ λγ increases λ −λ Sun z ≡ observed emitted λemitted

λobserved distant or 1+z = supercluster λemitted

See http://astro.unl.edu/classaction/animations/cosmology/galacticredshift.html

4 5 6 7 8 9 10 11 12 13 14 15 Different origins of /blueshifts

§ : redshift/blueshift due to relative motion

⎛ v // ⎞ v // 1+z =γ ⎜1+ ⎟ z ≈ for small v // ⎝ c ⎠ c (in i.e. flat )

§ Cosmological redshift : dominant for distant sources (above tens of Mpc or z>0.01). Due to Universe expansion.

§ Gravitational red/blue shift : radiation moving out of/into a gravitational field. 1 e.g. grav. redshift 1+z = 1−2GM rc 2 16

3. Expansion The rise of modern cosmology

Hubble, 1929

distant galaxies are receding : the Universe is in expansion (as predicted in by A.Friedmann 1922 and G.Lemaître 1927)

17 Hubble data Redshift converted into velocity z~v/c Hubble’s law

v =H0d § H0: Hubble constant

§ recent, precise measurements (2011): H0 =73.8±2.4km /s /Mpc

(2014): H 0 =70.6±3.3km/s/Mpc

(2018): H 0 =73.5±1.6km/s/Mpc

§ critical density today 0 2 2 10 −3 −1 −1 ρc =3H 0 8πG =1.04h 10 eV ⋅m h=H 0 100kms Mpc 3 3 X same energy density as 1gal/Mpc ~5p/m 18 Describing an expanding universe

§ General Relativity : the simplest relativistic theory of gravitaty consistent with data. Gravity described as a geometric property of spacetime.

§ Metric: allows to compute distances between two points 2 µ ν ds ≡ g µ ν dx dx 2 gµν : metric tensor ds : line element, invariant – Reminder: in (no gravity): 2 µ ν 2 2 2 2 2 ds ≡ηµνdx dx =c dt −dx −dy −dz =c 2dt 2 −(dr 2 +r 2 (dθ 2 +sinθ 2dϕ 2 )) ηµν : Minkowski metric – in a particle’s rest frame: ds = c d τ dτ : particle 19 § Friedmann-Lemaître-Robertson-Walker (FLRW) metric : metric for a spatially homogeneous and isotropic expanding universe, with scale/expansion factor a(t) and curvature k ⎛ dr 2 ⎞ ds 2 c 2dt 2 a (t )2 r 2 d 2 sin2 d 2 = − ⎜ 2 + ( θ + θ ϕ )⎟ ⎝1−kr ⎠

expansion factored out r,θ,ϕ spherical comoving a(t ) H ( t ) ≡ expansion rate or coordinates: a (t ) Hubble parameter r : dimensionless & H0 ≡H (t0 ) t0 =today stationary wrt expansion

k, gaussian curvature: closed flat open universe universe universe

k=+1 k=0 k=-1 20 More on FLRW metric dr § Introducing d χ ≡ to account for curvature : 1−kr 2

time

Δχ =3 D(t1 )=a(t1 )Δχ

Δχ =3 D(t2 )=a(t2 )Δχ ≥D(t1 ) a(t): scale factor χ: comoving coordinate, stationary wrt expansion D(t) : proper/physical distance Δχ: comoving distance 21

⎛ dr 2 ⎞ § FLRW metric: 2 2 2 ( )2 2 2 sin2 2 ds =c dt −a t ⎜ 2 +r (dθ + θdϕ )⎟ ⎝1−kr ⎠ ds 2 =c 2dt 2 −a (t )2 (dχ 2 +r 2 (dθ 2 +sin2θdϕ 2 )) ⎧ sinχ k =1 ⎪ r =f (χ)=⎨ χ k =0 ⎪ ⎩shχ k =−1

§ Hubble’s law: dD a(t ) dD D(t )=a (t )Δχ ⇒ =a(t )Δχ = D(t )⇒ =H (t )D(t ) dt a(t ) dt § Particle trajectories : ds 2 = 0 geodesic equation (shortest path in three- space and maximum proper time)

22 The cosmological redshift

Universe in expansion

light from distant sources is redshifted

λ a (t ) observed ≡1+z = observation λemitted a (temission )

X ©Ned Wright, UCLA 23 3. The Big Bang model Initial dense and hot phase More confirmations of the followed by expansion and cooling Big Bang model

Primordial nucleosynthesis (He, D): T~1MeV predicted light element abundances = data n −n B B ≈10-10 1948: G.Gamow, R.Alpher nγ Matter-radiation decoupling: z~1100 T~3000K Cosmic Microwave Background, relic radiation predicted and observed (T~2.725K 1992) 1948: G.Gamow, R.Alpher, R.Herman 1964: A.Penzias, R.Wilson

13,7 billions of years after Big Bang

1964 24 The rise of the Big Bang model

General Relativity, Einstein’s equations (1907-1915)

1922-1935 FLRW solutions (expanding, homogeneous and isotropic Universe)

1929 Hubble’s law 1948: Gamow et al: and CMB detection CMB predictions

1934: ‘missing mass’ in orbital velocities of galaxies in CMB primary anisotropies clusters → postulated (F.Zwicky)

ντ Accelerated expansion: (or modified Einstein’s gravity)

25 CONCLUSIONS (1)

§ The Universe is spatially homogeneous and isotropic on cosmological scales (above 100Mpc)

§ The Universe, initially in a hot, dense phase, is expanding

H 0 ≡H (ttoday )≈70km/s/Mpc • cosmological redshift: due to the Universe expansion

λ a (t ) observed ≡1+z = observation λemitted a (temission )

§ General relativity and FLRW metric are the basics of the Big Bang model

§ Observational confirmations: primordial abundances, CMB 26 Content of the Universe

From General Relativiy to the matter-energy content of the Universe

§ The Ωi parameters and the expansion history § Thermal history of the Universe

27 1. Densities ρi and Ωi parameters Big Bang cosmology model+ many cosmological data energy balance of the Universe

4.9% 68.5%

26.6%

ρ (t) Ω (t)≡ i CMB emission i ρc (t) 2018

1 = Ω (t ) + Ω (t ) + Ω (t ) + Ω (t ) m r k Λ NR matter radiation curvature “dark energy” negligible today or cosmological

constant Λ 28 0 Present values of the Ωi’s : the Ωi values 2.2% precision § CMB + BAO + SNe Ia data : 0 Ωm =0.315±0.007 0 ΩΛ =0.685±0.007 Planck collaboration. 2018, arXiv:1807.06209

Universe is flat !

atoms: gas (4%), stars (0.4%), ν (0.3%), heavy elements (0.03%) M. Kowalski et al., 2008, ApJ, 686, 749 29 The rise and fall of the Ωi’s

-4 -2 -3 -2 -2 Ωr∝a H Ωm∝a H ΩΛ∝H

z~3500 z~0.5 ? inflation

redshift z 30 2. Thermal history Expansion and temperature

§ Photons emitted at t (e.g. CMB), received today: at emission λ a E (t ) T (t ) 1+z ≡ observed = 0 = γ = λemitted a (t ) Eγ (t0 ) T0 today § Temperature was hotter in the past, expansion implies cooling down now −4 0 −5 § CMB now: TCMB ≈2.725K ⇒T 0 ≈2.35 10 eV ⇒Ωγ ≈5.10 −5 −1 (COBE) (k =8.617 10 eV .K ) negligible (today) § CMB at emission (from anisotropy measurements): emission zCMB ≈1100⇒TCMB (temission )≈0.26eV ≈3,000K § matter-radiation equality:

ρr (t eq )=ρm (t eq )⇒a 0 /a(t eq )⇒Teq ≈1eV z ≈3500

31 The CMB spectrum as seen by COBE (1989-1993)

CosmicSpectre Microwave du fond backgrounddiffus cosmologique spectrum selon COBEfrom COBE 400 DonnéesCOBE de COBE data Black Body spectrumSpectre de T corps=2.728K noir 350

300 TCMB = 2.728 ± 0.004 K

/sr) 250 Mjy

( 200

150 Intensité [MJy/sr]Intensité Intensity 100

50

0 2 4 6 8 10 12 14 16 18 20 22 FrequencyFréquence [1/cm](1/cm)

D.J. Fixsen et al. 1996, ApJ, 473, 576F

§ Final : TCMB = 2.7255 ± 0.0006 K D.J. Fixsen, 2009, AJ,707,916 32 Primordial nucleosynthesis

§ 1948: G.Gamow, R.Alpher "The origin of Chemical Elements" Expanding universe : deuterium and helium nuclei are formed by nuclear reactions inside the primordial plasma of p,n,e,γ when temperature and densities are adequate, leading to light element abundances as measured.

25%

0.01%

75%

measured primordial abundances 33 The evolution of abundances

tBBN~3mn : abundances frozen

-10 (η~10 assumed) 34 Present values of the Ωi’s

§ Measurements of light element abundances vs predictions: BBN 0 0.046≤Ωb ≤0.053 ( confirmed independently by CMB - Planck 2018 )

Most matter in the

nB −nB Universe is not ordinary η≡ CMB nγ atoms : dark matter ! M. Tanabashi et al. (PDG), Phys. Rev. D 98, 030001 (2018) 35 CONCLUSIONS (2)

§ Einstein GR equations + FLRW metric: 1 = Ω (t ) + Ω (t ) + Ω (t ) + Ω (t ) m r k Λ § COBE measurement: radiation today is negligible § Cosmological measurements vs predictions: – CMB+SNeIa+BAO: 0 Ωm =0.315±0.007 0 ΩΛ =0.685±0.007

èflat universe – Primordial abundances: 0 0.043≤Ωb ≤0.049

36 radiation matter-radiation equality domination T~0.83eV z~3500

D, 4He nucleosynthesis matter T~60keV z~108 domination 5 3mn 10 yr CMB 10-32s 380,000yr T~0.26eV z=1100 inflation ? BB 9Gyr 13.7Gyr

expansion acceleration today T~3.5 10-4eV z~0.5 T~2.35 10-4eV z=0

Λ domination 37