ИI ЯN ИR Cosmology: Lecture #1 Our Universe at present: main ingredients and the expansion law Dmitry Gorbunov Institute for Nuclear Research of RAS, Moscow 21 st European School on High-Energy Physics, CERN-JINR, Par´ adf¨ urd˝ o, Hungary, 06.06.2013 Dmitry Gorbunov (INR) Lecture #1 , 6 June 2013 06.06.2013, ESHEP 1 / 42
ИI ЯN ИR Standard Model: Success and Problems Gauge fields (interactions): γ , W ± , Z , g � u L � ν L � � Three generations of matter: L = , e R ; Q = , d R , u R e L d L Describes ◮ all experiments dealing with electroweak and strong interactions Does not describe ◮ Dark energy ( Ω Λ ) ◮ Neutrino oscillations ◮ Strong CP: ? (boundary ◮ Dark matter ( Ω DM ) terms, new topology, . . . ) ◮ Baryon asymmetry ( Ω B ) ◮ Gauge hierarchy: ? (No new scales!) ◮ Inflationary stage ◮ Quantum gravity Try to explain all above Planck-scale physics saves the day Dmitry Gorbunov (INR) Lecture #1 , 6 June 2013 06.06.2013, ESHEP 2 / 42
ИI Outline ЯN ИR Outline General facts and key observables 1 Evidences for Dark Matter in astrophysics and cosmology 2 Mystery of Dark Energy 3 Redshift and the Hubble law 4 Dmitry Gorbunov (INR) Lecture #1 , 6 June 2013 06.06.2013, ESHEP 3 / 42
ИI Outline ЯN ИR “Natural” units in particle physics h = c = k B = 1 ¯ measured in GeV: energy E , mass M , temperature T 1 K = 8 . 6 × 10 − 14 GeV m p = 0 . 938 GeV, measured in GeV − 1 : time t , length L 1 s = 1 . 5 × 10 24 GeV − 1 , 1 cm = 5 . 1 × 10 13 GeV − 1 Gravity (General Relativity): V ( r ) = − G m 1 m 2 [ G ] = M − 2 r M Pl = 1 . 2 × 10 19 GeV = 22 µ g 1 G ≡ M 2 Pl Dmitry Gorbunov (INR) Lecture #1 , 6 June 2013 06.06.2013, ESHEP 4 / 42
ИI Outline ЯN ИR “Natural” units in cosmology 1 Mpc = 3 . 1 × 10 24 cm 1 AU = 1 . 5 × 10 13 cm mean Earth-to-Sun distance 1 ly = 0 . 95 × 10 18 cm distance light travels in one year 1 yr = 3 . 16 × 10 7 s 1 pc = 3 . 3 ly = 3 . 1 × 10 18 cm distance to object which has a parallax angle of one arcsec 100 AU — Solar system size 1.3 pc — nearest-to-Sun stars 1 kpc — size of dwarf galaxies 50 kpc — distance to dwarves 0.8 Mpc — distance to Andromeda 1-3 Mpc — size of clusters 15 Mpc — distance to Virgo Dmitry Gorbunov (INR) Lecture #1 , 6 June 2013 06.06.2013, ESHEP 5 / 42
ИI General facts and key observables ЯN ИR Outline General facts and key observables 1 Evidences for Dark Matter in astrophysics and cosmology 2 Mystery of Dark Energy 3 Redshift and the Hubble law 4 Dmitry Gorbunov (INR) Lecture #1 , 6 June 2013 06.06.2013, ESHEP 6 / 42
ИI General facts and key observables ЯN ИR Universe is expanding L ∝ a ( t ) Doppler redshift of light n ∝ a − 3 ( t ) H ( t ) = ˙ a ( t ) a ( t ) Hubble parameter Hubble Law H ( t 0 ) r = v r Dmitry Gorbunov (INR) Lecture #1 , 6 June 2013 06.06.2013, ESHEP 7 / 42
ИI General facts and key observables ЯN ИR Expansion: redshift z λ abs . / λ em . ≡ 1 + z z ≪ 1 Hubble law : z = H 0 r km H 0 = h · 100 h = 0 . 705 ± 0 . 015 s · Mpc Dmitry Gorbunov (INR) Lecture #1 , 6 June 2013 06.06.2013, ESHEP 8 / 42
ИI General facts and key observables ЯN ИR Expansion: redshift z λ abs . / λ em . ≡ 1 + z z ≪ 1 Hubble law : z = H 0 r km H 0 = h · 100 h = 0 . 705 ± 0 . 015 s · Mpc standard candles Dmitry Gorbunov (INR) Lecture #1 , 6 June 2013 06.06.2013, ESHEP 9 / 42
ИI General facts and key observables ЯN ИR Universe is homogeneous and isotropic redshift h 1 h 0 h 2 h RA 23 z ≡ λ detector λ source − 1 3 h h 22 h 4 21 h -39 o o -42 -45 o 60 Dec 50 40 30 South cz (1000 km/s) 20 12434 galaxies ← 150 Mpc v r = c z 10 Dmitry Gorbunov (INR) Lecture #1 , 6 June 2013 06.06.2013, ESHEP 10 / 42
ИI General facts and key observables ЯN ИR The Universe: age & geometry & energy density [ H 0 ] = L − 1 = t − 1 ≈ 14 × 10 9 yr time scale: t H 0 = H − 1 age of our Universe 0 ≈ 4 . 3 × 10 3 Mpc spatial scale: l H 0 = H − 1 size of the visible Universe 0 t H 0 is in agreement with various observations homogeneity and isotropy in 3d : flat, spherical or hyperbolic Observations: “very” flat l H 0 / R curv < 0 . 1 GM U / l U ∼ G ρ 0 l 3 order-of-magnitude estimate: H 0 / l H 0 ∼ 1 flat Universe ρ c = 3 Pl ≈ 0 . 53 × 10 − 5 GeV 8 π H 2 0 M 2 → 5 protons in each 1 m 3 − cm 3 Dmitry Gorbunov (INR) Lecture #1 , 6 June 2013 06.06.2013, ESHEP 11 / 42
ИI General facts and key observables ЯN ИR Universe is occupied by “thermal” photons T 0 = 2 . 726 K the spectrum Wavelength (cm) 10 − 17 10 1.0 0.1 (shape and normalization!) 10 − 18 is thermal I ν (W m − 2 sr − 1 Hz − 1 ) 10 − 19 n γ = 411 cm − 3 2.726 K blackbody 10 − 20 FIRAS� COBE satellite� DMR� COBE satellite� UBC� sounding rocket� 10 − 21 LBL-Italy� White Mt. & South Pole� Princeton� ground & balloon� Cyanogen optical 10 − 22 1 10 100 1000 Frequency (GHz) Dmitry Gorbunov (INR) Lecture #1 , 6 June 2013 06.06.2013, ESHEP 12 / 42
ИI General facts and key observables ЯN ИR Conclusions from observations The Universe is homogeneous, isotropic, hot and expanding... Conclusions interval between events gets modified ∆ s 2 = c 2 ∆ t 2 − a 2 ( t )∆ x 2 1 h 0 h 2 h 23 h RA 3 h 22 h 4 h 21 h -39 o in GR expansion is described by the Friedmann equation -42 o -45 o 60 Dec 50 40 � ˙ � 2 30 a = H 2 ( t ) = 8 π South cz (1000 km/s) 3 G ρ energy 20 12434 galaxies 10 density a ρ energy density = ρ radiation + ρ matter + ... Wavelength (cm) 10 − 17 10 1.0 0.1 in the past the matter density was higher, our Universe was 10 − 18 I ν (W m − 2 sr − 1 Hz − 1 ) “hotter” filled with electromagnetic plasma 10 − 19 2.726 K blackbody 10 − 20 FIRAS� COBE satellite� DMR� COBE satellite� ρ matter ∝ 1 / a 3 ( t ) , ρ radiation ∝ 1 / a 4 ( t ) , ρ curvature ∝ 1 / a 2 ( t ) UBC� sounding rocket� 10 − 21 LBL-Italy� White Mt. & South Pole� Princeton� ground & balloon� Cyanogen optical 10 − 22 1 10 100 1000 Frequency (GHz) certainly known up to T ∼ 1MeV ∼ 10 10 K Dmitry Gorbunov (INR) Lecture #1 , 6 June 2013 06.06.2013, ESHEP 13 / 42
ИI General facts and key observables ЯN ИR Why do we need dark components (within GR)? Astrophysical data favor Dark Matter ◮ Observations in galaxies ◮ Observations in galaxy clusters Cosmological data favor Dark Matter and Dark Energy ◮ Observation of objects at cosmological distances (far=early) ◮ Baryonic Aciustic (Sakharov) Oscillations (BAO) in two-point galaxy correlation function ◮ Evolution of galaxy clasters in the Universe ◮ Anisotropy of Cosmic Microwave Background (CMB) Dmitry Gorbunov (INR) Lecture #1 , 6 June 2013 06.06.2013, ESHEP 14 / 42
ИI Evidences for Dark Matter in astrophysics and cosmology ЯN ИR Outline General facts and key observables 1 Evidences for Dark Matter in astrophysics and cosmology 2 Mystery of Dark Energy 3 Redshift and the Hubble law 4 Dmitry Gorbunov (INR) Lecture #1 , 6 June 2013 06.06.2013, ESHEP 15 / 42
ИI Evidences for Dark Matter in astrophysics and cosmology ЯN ИR Astrophysical and cosmological data are in agreement 2.0 � ˙ � 2 a = H 2 ( t ) = 8 π No Big Bang 3 G ρ energy density a ρ energy density = ρ radiation + ρ ordinary + ρ dark matter + ρ Λ matter 1.5 ρ radiation ∝ 1 / a 4 ( t ) ∝ T 4 ( t ) , ρ matter ∝ 1 / a 3 ( t ) ρ Λ = const 3 H 2 density ( t 0 ) ≡ ρ c ≈ 0 . 53 × 10 − 5 GeV 1.0 8 π G = ρ energy 0 cm 3 SNe Ω γ ≡ ρ γ ρ c = 0 . 5 × 10 − 4 radiation: Ω B ≡ ρ B Baryons (H, He): ρ c = 0 . 046 0.5 ∑ ρ ν i Neutrino: Ω ν ≡ < 0 . 01 ρ c CMB Flat Ω DM ≡ ρ DM BAO Dark matter: ρ c = 0 . 23 Ω Λ ≡ ρ Λ 0.0 Dark energy: ρ c = 0 . 73 0.0 0.5 1.0 Dmitry Gorbunov (INR) Lecture #1 , 6 June 2013 06.06.2013, ESHEP 16 / 42
ИI Evidences for Dark Matter in astrophysics and cosmology ЯN ИR Galactic dark halos: flat rotation curves � GM ( R ) v ( R ) = R � R 0 ρ ( r ) r 2 dr M ( R ) = 4 π observations: v ( R ) ≃ const √ visible matter: internal regions v ( R ) ∝ R √ external (“empty”) regions v ( R ) ∝ 1 / R Dmitry Gorbunov (INR) Lecture #1 , 6 June 2013 06.06.2013, ESHEP 17 / 42
ИI Evidences for Dark Matter in astrophysics and cosmology ЯN ИR Dark Matter in clusters X -rays from hot gas in clusters � R dP GM ( R ) 0 ρ ( r ) r 2 dr , dR = − µ n e ( R ) m p , M ( R ) = 4 π P ( R ) = n e ( R ) T e ( R ) R 2 galaxies in clusters virial theorem U + 2 E k = 0 r � = GM 2 3 M � υ 2 R Milky Way: Virgo infall Dmitry Gorbunov (INR) Lecture #1 , 6 June 2013 06.06.2013, ESHEP 18 / 42
ИI Evidences for Dark Matter in astrophysics and cosmology ЯN ИR Gravitational lensing in GR: α = 4 GM / ( c 2 b ) Einstein Cross η = D s � � � � � ξ − D ls � α ξ D l common lens with specific refraction coefficient ξ − � � ξ ′ source: quasar D s = 2 . 4 Gpc = 4 G � � � � � 2 d 2 ξ ′ � � ξ ′ , z � � α ξ ρ dz c � � � ξ − � ξ ′ � � lens: galaxy D l = 120 Mpc � Dmitry Gorbunov (INR) Lecture #1 , 6 June 2013 06.06.2013, ESHEP 19 / 42
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