The expanding universe. Lecture 2

Transcription

1 The expanding universe Lecture 2

2 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 Expanding Universe 2

3 Last lecture Universe is flat k=0 Expansion dynamics is described by Friedman-Lemaître 2 equation 2 2 R () t 8π GN c H( t) = otρ () t kt 2 R t ( ) 3 ( R ( t ) ) Cosmological redshift R( t0 ) 1 z z( t0 ) 0 z( t 0) R ( t ) Closure parameter ( t ) + = = = = ρ ρ () t () t Ω = ρ ( t ) 0 Expansion rate as function of redshift c 2 3H ρ c t = GeV m πg = 8 N 2 ( ) = ( t )( 1+ ) + Ω ( )( 1+ z ) + Ω ( t ) + Ω ( )( 1+ z ) H t H 0 0 z t 0 0 t 0 Ω m r Λ k Expanding Universe 3

4 Ω rad Part 4&6 Todays lectur re Ω baryons Part 7 Ω neutrino Part 5 Ω CDM Part 5 Rubakov Expanding Universe 4

5 Part 4 radiation component - CMB Physics of the Cosmic Microwave Background Present day radiation density

6 Cosmic Microwave Background photons

7 CMB in Big Bang model In early hot universe, when z > 1100 radiation dominates over matter vacuum energy is negligible As soon as kt ~ few MeV Weak interactions are too weak & neutrinos decouple Remain with free p, n, e, g (+neutrino s) Big Bang Nucleosynthesis starts: e+ γ e + γ formation of H, D, He, Li nuclei n + p D +γ Plasma of p, n, e, light nuclei and photons in thermal equilibrium When kt < ev (ionisation potentials) : recombination to atoms - photons decouple e + p H +γ Expanding Universe 7

8 CMB in Big Bang model Matter photons are released Univ Oregon Baryons/nuclei and photons in thermal equilibrium Photons decouple/freeze-out out During expansion they cool down Expect to see today a uniform γ radiation which behaves like a black body radiation Expanding Universe 8

9 CMB discovery in 1965 discoveredd in 1965 by Penzias and dwil Wilson (Bell lllabs) when searching for radio emission from Milky Way Observed a uniform radio noise from outside the Milky Way This could not be explained by stars, radio galaxies etc Use Earth based observatory: limited to cm wavelengths due to absorption of mm waves in atmosphere Observed spectrum was compatible with black body radiation with T = (3.5 ±1) K Obtained the Nobel Prize in 1978 ( Expanding Universe 9

10 COBE : black body temperature To go down to mm wavelengths : put instruments on satellites COBE = COsmic Background Explorer (NASA) satellite observations in 1990s: mm wavelengths Large scale dipole anisotropy due to motion of solar system in universe, with respect to CMB rest frame v ( solar system) 300 km s Strong radio emission in galactic plane After subtraction of dipole and away from galactic centre: radiation was uniform up to 0.005% Has perfect black body spectrum with T = 2.735± K K (COBE 1990) Discovered small anisotropies/ripples over angular ranges Dq= Nobel prize to Smoot and Mather for discovery of anisotropies Expanding Universe 10

11 CMB temperature map dipole ΔT smallll ripples i l on top t off Black Bl k Body B d radiation: di ti ΔT T T 10 3 O ( mk ) 10 5 O ( µk ) Contrast enhanced to make 10-5 variations visible! Expanding Universe 11

12 COBE measures black body spectrum l=2mm Intensity Q 0.5mm Plancks radiation law for relativistic photon gas Black body with temperature T emits radiation with power Q at frequencies w Frequency n (cm -1 ) Q ω, T ( ) ω = 2πν = 4π c ω ω e k T Expanding Universe 12

13 COBE measures black body spectrum l=2mm Intensity Q 0.5mm CMB has perfect black body spectrum Fit of data of different observatoria to black body spectrum gives ( ) = ( ± ) ( max) = 2mm T CMB λ Or E = kt = mev K Frequency n (cm -1 ) Expanding Universe 13

14 CMB energy density vs time In our model the early universe is radiation dominated For flat universe Friedmann equation R 8π G 2 N = 2 R 3 energy density of radiation during expansion ρ rad ρ rad 1+ z R ( ) 4 4 Integration yields ρ 1 dρ 4R 8πG 4 N ρrad = = ρ dt R 3 rad c 2 t () = 2 3c 1 32π GN t Expanding Universe 14

15 CMB number density today 1 CMB photons have black body spectrum today They also had black body spectrum when CMB was created But! Temperature T in past was higher than today CMB = photon gas in thermal equilibrium Bose-Einstein distribution : number of photons per unit volume in momentum interval g[p,p+dp] 2 γpdp n( p) dp= 2 g γ = number of 2 3 e E k π T 1 photon substates Black body Expanding Universe 15

16 CMB number density today 2 n N V γ γ = = g γ =2 n p dp ( ) 1 kt n γ = π c T=2.725K 3 n t0 411cm γ = exercise ( ) Expanding Universe 16

17 CMB energy density today ρ c 2 = E n p dp ( ) ρ ( ) r c t 0 = MeV m 2 3 ρ Ω ( ) r r t0 = = ρ ρ c 5 exercise Expanding Universe 17

18 CMB temperature vs time ρ rad c 2 = 2 3c 1 2 4( ) 4 γ 1 2 ρ radc = π kt πg t 2 15 π c 32 N g kt c 2 1 = π G g γ t 2 10 cst T = rad dom 2for t 0 = 14Gyr expect T CMB (today) ª 10K!!! t BUT! From COBE measures T = 2.7K Explain! Expanding Universe 18

19 Exercise 1 Discussion during exercise session of 30 March To be handed in to Erik Strahler before 20 April exercise Problem 1: proove that today the number density of CMB photons and their energy density are 3 n ( t ) = 411cm CMB 0 ρ ( 0 ) = Ω ( t ) CMB c t MeV m CMB t Proove that their temperature today should be 2.7K Are there other particles besides the CMB photons which contribute to Ω rad today? Expanding Universe 19

20 Part 5 particle physics in the early universe Radiation dominated universe From end of inflation to matter-radiation decoupling From ~ GeV to ev Physics beyond the Standard Model, SM, nuclear physics Ω CDM, Ω ν

21 Radiation domination era Planck era At end of inflation phase there is a reheating phase Relativistic particles are created Expansion is now radiation dominated Hot Big Bang evolution starts R kt TeV GUT era Expanding Universe 21 t

22 Planck era kt Today s lecture R GUT era Expanding Universe 22 t

23 Planck mass Grand TeV ~ GeV Unification LEP-LHC ~ GeV Inflation period Expanding Universe 23

24 Today s lecture Planck mass Grand TeV ~ GeV Unification LEP-LHC ~ GeV Inflation period Expanding Universe 24

25 relativistic particles in early universe In the early hot universe relativistic fermions and bosons contribute to the energy density They are in thermal equilibrium Fermion gas = quarks, leptons Fermi-Dirac statistics (g f = nb of substates) ( ) n p dp g f 2 p dp = E 2 3 kt 2 π e 1 + boson gas = photons, W and Z bosons Bose Einstein statisticss n ( p ) dp π (g b = nb of substates) g b 2 p dp = E 2 3 kt 2 e Expanding Universe 25

26 relativistic particles in early universe Bosons and fermions contribute to energy density with ( ) n p dp 2 pdp g 2 = b p dp g E 2 3 kt 2 ( ) f n p dp= E π e kt 2 π e 1 + ρ 2 ρ c = E ( ) n p dp g( ( ) π ( ) = = + 15π c * * c t kt g g b g f * T = thermodynamic temperature of black body Expanding Universe 26

27 Degrees of freedom for kt > 100 GeV If we take only the known particles bosons spin per particle total t W+ W- Z gluons photon Higgs total bosons 28 fermions spin per particle total quarks antiquarks e,µ,τ neutrinos anti-neutrinos total fermions Expanding Universe 27

28 Degrees of freedom for kt > 100 GeV bosons spin per particle total W+ W x3=6 Z gluons x 2 = 16 photon Higgs total bosons 28 fermions spin per particle total quarks ½ 3 (color) x 2 (spin) 6 x 3 x 2 = 36 antiquarks 36 e,µ,τ ½ 2 6 x 2 = 12 neutrinos LH 1 3 x 1 = 3 anti-neutrinos RH 1 3 x 1 = 3 total fermions Expanding Universe 28

29 Degrees of freedom for kt > 100 GeV Assuming only particles from Standard Model of particle physics g = = * 7 Energy density in hot universe *( ) ( ) ρ* c t = π kt π c 2 g what happens if there were particles from theories beyond the Standard Model? Expanding Universe 29

30 For instance : SuperSymmetry At LHC energies and higher : possibly SuperSymmetry Symmetry between leptons and bosons Consequence is a superpartner for every SM particle Double degrees of freedom g* Expanding Universe 30

31 Neutralino = Dark Matter? Neutral gaugino and higgsino fields mix to form 4 mass eigenstates 4 neutralinos no charge, no colour, only weak and gravitational interactions χ is Lightest t Supersymmetric Particle LSP - in R-parity conserving scenarios stable Massive : Searches at LEP and Tevatron colliders m ( ) χ 0 > 50 GeV c Expanding Universe 31

32 Neutralino = Dark Matter? Lightest neutralino may have been created in the early hot universe when ( χ ) 1 2 kt >> m c > 50 GeV Equilibrium interactions e + e χ 0 + χ0 When kt is too low, neutralinos freeze-out (decouple) e + e χ + χ 0 0 Heavy are non-relativistic at decoupling = cold survive as independent population till today the observed dark matter abundance today puts an upper limit on the mass (chapter 7) ρ < ρ < ρ m χ 1 < 5 TeV c 2 baryon CDM critical ( ) Expanding Universe 32

33 Cool down from > TeV to kt ª GeV Start from hot plasma of leptons, quarks, gauge bosons, Higgs, exotic particles Temperature decreases with time T 1 rad dom ~ 1 2 Production of particles M stops when kt t Mc For example, + + e + e W + W when s > 2MW = 160GeV p + p t+ t when > 2 = 346 s M GeV 23 Most particles decay: W, Z, t, b, τ,.. τ ( W, Z) 10 Run out of heavy particles when kt<<100gev Expanding Universe 33 top s 2

34 Down to kt ª 200 MeV Phase transition from Quark Gluon Plasma (QGP) to hadrons Ruled by Quantum Chromo Dynamics (QCD) of strong interactions Strong coupling constant is running : energy dependent From perturbative regime to non-perturbative regime around Λ QCD α S ( 2 2 μ Q ) = 2 gstrong 1 4π b ln μ Cln ( μ ) μ E T Dconfinement Λ = QCD 200MeV From fit to data Quarks cannot be free at distances of more than 1fm = m Expanding Universe 34

35 Colour confinement large distances Asymptotic freedom small distances Expanding Universe 35

36 around and below kt ª 200 MeV free quarks and gluons are gone and hadrons are formed Most hadrons are short lived and decay with τ ( ) s( ) = 10 8 s weak ints strong ints. << 1µs Example ( ) ( ) Λ 1115 = uds p + π p + μ + ν Leptons : muon and tauon decay weakly τ μ = 2 10 ( ) 6 s μ e + ν + ν μ e n π n+ e e 15 ( ) = τ τ s τ μ + ν + ν... μ μ Stable or long lived τ ( 17% ) Expanding Universe 36

37 Cooldown to kt ª few 10MeV After about 1ms all unstable particles have decayed Most, but not all, nucleons annihilate with anti-nucleons (chapter 6) γ + γ p+ p 18 n baryons n γ * 7 43 g = = 4 g* GeV 10 MeV we are left with g + e -, n e e, n m m,, n t and their anti-particles TeV kt(gev) Expanding Universe 37

38 Around kt MeV: Big Bang Nucleosynthesis around few MeV: mainly relativistic g, e,n e, n m, n t + antiparticles in thermal equilibrium + few protons & neutrons weak interactions ν e + n e + p ν e + + p e + n n p+ e + ν ( ) e + + e i + i γ ν ν start primordial nucleosynthesis: formation of light nuclei (chapter 6) 2 n+ p H + γ MeV 2 H H 3 + n H e γ + H He + γ Expanding Universe 38

39 Around kt 3MeV : Neutrino freeze out Equilibrium between photons and leptons + γ e + e ν ν i e μ τ ( ),, + = Weak interaction i i Weak interaction cross section decreases with energy σ G 2 F s 6π s = CM energy G = F GeV Expanding Universe 39

40 Neutrino freeze-out at t 1s + e e ν ν i e, μ, τ + + = Weak interaction i i e+e- e collision rate interactions/sec W = n σ v e+, relative e- number density Cross section Relative (FD statistics) ~ T 3 ~ s ~ T 2 velocity H t 5 2 During expansion T decreases ( ) W when W << H or kt < 3MeV or t > 1s T Neutrinos no longer interactt Neutrinos decouple and evolve independently neutrino freeze-out Æ relic neutrinos Expanding Universe 40 T

41 Cosmic Neutrino Background Relic neutrinos are oldest relic of early universe decoupled at about 1s before CMB photons Should be most abundant particles in sky after CMB photons Should populate universe today as Cosmic Neutrino Background CνB or cosmogenic neutrinos what are numbers density and temperature today? Expanding Universe 41

42 Cosmic Neutrino Background At few MeV there was thermal equilibrium between photons and leptons + ( γ ) e + e νi + νi i= e, μ, τ Number density neutrinos ª number density photons expected Temperature of neutrinos today T ( t ) 1.95K ν 0 = ν 0 E ( t ) mev expected density of relic neutrinos today: for given species (n e, n m, n t ) 3 3 N + N = N = 113 cm ν ν 11 CνB could explain part of Dark Matter : weakly interacting, massive, stable is Hot DM (chapter 7) Ω γ ν Expanding Universe 42

43 Exercise 2 Discussion during exercise session of 30 March To be handed in to Erik Strahler before 20 April exercise problem 2 Solve problem 5.12 in Particle Astrophysics (D. Perkins) Derive for the neutrinos from the CνB : Number density today Energy density today Temperature today Ω neutrino today Were these neutrinos ever observed? Howcould one detect them? Expanding Universe 43

44 Relativistic particles in early times Quarks confined in hadrons g* 10 Neutrino Decoupling and nucleosynthesis Run out of relativistic particles ep recombination 3.4 Transition to GeV MeV matter dominated universe TeV kt(gev) Expanding Universe 44

45 Part 6 matter and radiation decoupling Recombination of electrons and protons to H atoms at Z ~ 1100

46 Radiation-matter decoupling At t dec ª years, or z ª1100, or T ª 3500K matter decouples from radiation and photons can move freely & remain as today s CMB radiation Matter evolves independently - atoms & molecules are formed stars, galaxies, If spatial temperaturet variations are present leave imprint on CMB (see chapt 8) Before t dec universe is ionised and opaque Population consists of p, H, e, g + light nuclei + neutrinos Expanding Universe 46

47 Protons and neutral hydrogen Up to t ª y thermal equilibrium of p, H, e, g e + p H + γ Depends on densities formation of neutral hydrogen of free e and p ionisation of hydrogen atom N e and N p Photon density much higher than proton density observations 10 N γ 10 N N p = N e p When kt < I=13.6 ev (ionisation potential of H) number of photons with E(γ)>I reduces Ionisation probability reduces Expanding Universe 47

48 Protons and neutral hydrogen number density of free protons N p and of neutral hydrogen atoms N H as function of T H N p N H + 1 2π mkt = = 2 NH NH Ne h 3 2 e I kt N e = density of free electrons m=electron mass Expanding Universe 48

49 Radiation-matter decoupling Rewrite in function of fraction x of ionised hydrogen atoms x N = = N + N N p N 2 p p H B x 1 2π mk T = 2 x N h 1 B strong drop of x between kt ª ev or T between K fi ionisation stops around 3500K period of recombination of e and p to hd hydrogen atoms e + p H + γ Stops when electron density too small 3 2 e I kt Expanding Universe 49

50 Decoupling time Reshift at decoupling R( t ) ( ) Full calculation ( ) + ktdec 3500 z dec = R t = = z = 1100 dec ( ) kt 0 dec tdec = When electron density is too small there is no H formation anymore Photons freeze out as independent population = CMB 5 y start of matter dominated universe We are left with atoms, CMB photons and relic neutrinos + neutralinos if SuperSymmetry describes nature at high T Expanding Universe 50

51 Era of matter-radiation equality since 3 Ω T 4 Ω T baryonic matter photons Density of baryons = density of photons when Ω ( ) ( ) bar t bar t0 1 1 Ω t = Ω Ω t 1+ z = 1+ z = 870 ( 1+ z ) dec phot () phot ( ) 0 Density of matter (baryons + Dark Matter) = density of photons + neutrinos when Ω () ( ) matter t Ωm t0 1 = = 1 Ω z Ω ( t ) Ω ( t ) phot+ neut Ω phot 0 1+ z 3130 Matter dominates over relativictic particles when Z < Expanding Universe 51

52 Summary Ene ergy pe er partic cle T(K) Time t(s) Expanding Universe 52

53 Part 7 (chapter 6) Big Bang Nucleosynthesis synthesis of light elements when kt ~ MeV Observation of light element abundances Baryon/photon ratio

54 Overview 1 at period of neutrino decoupling when kt ~ 3MeV e +, e γ, p, n, p,, n ( e, μτ ), νν,, Anti-particles are annihilated particles remain (part 8) e + + e ν + ν i i p + p γ + γ Nγ N Fate of baryons? Big Bang Nucleosynthesis model Protons and neutrons in equilibrium due to weak + interactions ν e + p e + n n p + e + ν e Due to cooling neutron population decreases Neutrons are saved by binding to protons deuterons n+ p D+ γ MeV Expanding Universe 54 BAR

55 Overview 2 When kt << I(D)=2.2 2 MeV dissociation i of D stops At kt ~ 80 KeV (20 mins) all neutrons are bound in nuclei Onset of primordial nucleosynthesis formation of nuclei H, H, He, He, Be, Li model of BBN predicts abundances of flight elements today At recombination ( y) nuclei + e - atoms + CMB photons e + p H + γ CMB Atoms form stars, Large Scale Structures (LSS) 10 N baryon Consistency of model: η10 10 N photon light element abundances? =? η CMB and LSS observations depend on 10 light elem η10 CMB, LSS ( ) ( ) Expanding Universe 55

56 Big Bang or primordial nucleosynthesis Fusion processes occuring between kt ª 3 MeV & ktª80 KeV Before tª y, in radiation dominated universe synthesis of light elements: It is NOT H, He, He, Be, Li the synthesis of elements in stars taking place during star formation and evolution in the matter dominated universe after y Expanding Universe 56

57 neutron proton equilibrium When kt ~ 3 MeV neutrinos decouple from e, γ particle population consists of + e, e, νν, ( e, μτ, ) Most anti-particles are annihilated + e + e ν + ν i p + p γ + γ Tiny fraction of nucleons is left Protons and neutrons in equilibrium due to weak interactions with neutrinos And neutron decay t = (885.7 ± 0.8)s i γ, p, n, pn, ν e e + n e + + p ν + p e + n n p + e + ν Weak interactions stop when W << H n & p 5 ( ) = σ W t n v T H t T ( ) 2 e Expanding Universe 57

58 neutron/proton ratio vs Temperature As soon as kt << 1 GeV nucleons are non-relativistic Probablity that proton is in energy state in [E,E+dE] P During equilibrium between weak interactions at nucleon freeze-out time t FO kt ~ 0.8MeV During whole process neutrons can decay with t = (885.7 ± 0.8)s proton kt < M c E M p c 2 e kt = exp kt ( ) 2 Mc2 Mn M p c Δ N n = exp = e N p kt N n ( t ) FO N p ( t ) FO = ( ) exp ( τ ) () exp( τ ) Nn t t = Np t t p 2 kt Expanding Universe 58

59 T(keV) weak interactions in equilibrium N t ( ) n () N t p 0.8MeV Start fusion to D 1s 80 KeV Nuclear reactions dominate Start of BBN 1min Steigman 2007 t(s) t(s) Expanding Universe 59

60 Nucleosynthesis onset Non-relativistic neutrons also form atoms through fusion: formation of deuterium 2 n + p H + γ MeV formation of 2 desintegration of H Photodisintegration of 2 H stops when kt 80 KeV << I(D)=2.2MeV free neutrons are gone And deuterons freeze-out 2 H N n N N p n = Expanding Universe 60

61 Nuclear chains Chain of fusion reactions 2 n+ p H + γ MeV Production of light nuclei 2 3 H + n H + γ 2 H H H 3 He + γ e2 2 + H + γ H + H He+ n He He 7 B L7 + +7i + e + γ Be n p ΛCDM model predicts values of relative ratios of light elements We expect the ratios to be constant over time Comparison to observed abundances today allows to test the standard cosmology model Expanding Universe 61

62 He mass fraction helium mass fraction Y ( ) 4y 2 ( N ) n Np ( 1+ ) n p M He = = = M He H y N N ( ) ( ) y = N N He H Is expected to be constant with time He in stars (formed long time after BBN) has only small contribution model prediction at onset of BBN (kt ª80keV, N n/n pª0.13 ) Y 0.25 pred Observation today in clusters, gas clouds Y = ± obs Expanding Universe 62

63 Abundances of light elements Standard BB nucleosynthesis theory predicts abundances of light elements today example Deuterium Observations today D 5 ( DH ) 10 H = ± 4 BBN 10 Starts ktª80kev η 10 t(s) Abundances depend on baryon/photon ratio Expanding Universe 63

64 Baryon/photon ratio ratio of baryon and photon number densities Baryons = atoms N baryon Photons = CMB radiation η N photon In standard model : ratio is constant since BBN era (kt~80 kev, t~20mins) Should be identical at recombination time (t~ y) 000y) Observations : abundances of light elements, He mass fraction t~20mins CMB anisotropies from WMAP t~ y Expanding Universe 64

65 Abundances and baryon density W B h 2 B Observations Of light elements He mass fraction Measure η 10 CMB observations with WMAP measure W B h 2 abundances Model Predictions Depend on η 10 W B h 2 η Expanding Universe 10 65

66 Y p = ± Best fit results PDG ( ) 10 ( ) D / H = ± Li / H = 1.7 ± 0.06 ± Ω = ± B N B N γ 10 ( ) 10 η = = ± pdg.lbl.gov g Expanding Universe 66

67 Part 8 (chapter 6) baryogenesis Where did the anti-matter go?

68 What about antimatter? Antiparticles from early universe have disappeared! Early universe: expect equal amount of particles & antiparticles because all interactions conserve CP expect that since matter-radiation decoupling ( + ) ( N e = N e ) N( p) = N( p) primary charged galactic cosmic rays: detect nuclei and no antinuclei Annihilation of matter with antimatter in galaxies would yield intense X-ray and g-ray emission not observed Few positrons and antiprotons fall in on Earth atmosphere : in agreement with pair creation in inter-stellar matter Antiparticles produced in showers in Earth atmosphere = secundary cosmic rays Expanding Universe 68

69 Baryon number conservation Violation of baryon number conservation would explain baryon - anti-baryon asymetry Baryon number conservation = strict law in laboratory If no B conservation Æ proton decay allowed p e + ν e Some theories of Grand Unification allow for baryon number non-conservation Search for proton decay in e.g. SuperKamiokande p 0 e + π τ p > 10 Lower limit on lifetime ( ) 33 y Expanding Universe 69

70 Baryons and antibaryons Assume net baryon number = 0 in early universe Assume equilibrium between photons and baryons p + p γ + γ Around MeV interaction rate W << H residu of baryons and antibaryons freeze-out N N N B = 10 N B 18 γ γ exercise Uitwerking meebrengen op examen Expanding Universe 70

71 Baryons and antibaryons Expect today in Big Bang model N B = 10 N N 18 N B γ γ Observe N B 10 9 ( ) η = = ± N N B N B γ < 10 4 Eplanation? Explanation? Expanding Universe 71

72 Baryon-antibaryon asymmetry Is the model wrong? Proposal by Zacharov : 3 fundamental conditions for asymmetry in baryon anti-baryon density: start from initial B=0 followed by Baryon number violating interactions Non-equilibrium situation leading to baryon/anti-baryon asymetry CP and C violation: anti-matter different reactions than matter Eg in Grand Unified Theories proton can decay Search at colliders for violation of fc and CP conserving interactions Expanding Universe 72

73 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 Expanding Universe 73