Introduction. How did the universe evolve to what it is today?

Transcription

1 Cosmology 8 1

2 Introduction 8 2 Cosmology: science of the universe as a whole How did the universe evolve to what it is today? Based on four basic facts: The universe expands, is isotropic, and is homogeneous. Isotropy and homogeneity of the universe: cosmological principle. Perhaps (for us) the most important fact is: ( anthropic principle ) The universe is habitable for humans. The one question cosmology does not attempt to answer is: How came the universe into being? = Realm of theology! Introduction 1

3 Edwin Hubble 8 3 Edwin Hubble ( ): Realisation of galaxies as being outside of the Milky Way Discovery that universe is expanding Founder of modern extragalactic astronomy Christianson, 1995, p. 165 Expansion of the Universe 1

4 Redshifts, I 8 4 Hubble: spectral lines in galaxies are more and more redshifted with increasing distance. Expansion of the Universe 2

5 Redshifts, II 8 5 Redshift: z = λ observed λ emitted λ emitted interpreted as velocity: v = cz where c = km s 1 (speed of light) 2dF QSO Redshift survey Expansion of the Universe 3

6 Hubble Relation 8 6 Hubble relation (1929): The redshift of a galaxy is proportional to its distance: v = cz = H 0 d where H 0 : Hubble constant. Measurement: determine v from redshift (easy), d with standard candles (difficult) = H 0 from linear regression. Hubble Space Telescope finds H 0 = 72 ± 8 km s 1 Mpc 1 (Freedman, 2001, Fig.4) Discussions in previous years on value of H 0 are over... Expansion of the Universe 4

7 Homogeneity 8 7 2dF Survey, galaxies total Homogeneity: The universe looks the same, regardless from where it is observed (on scales 100 Mpc). Expansion of the Universe 5

8 Isotropie 8 8 Isotropy The universe looks the same in all directions. Peebles (1993): Distribution of radio sources on northern sky (wavelength λ = 6 cm) N.B. Homogeneity does not imply isotropy, and isotropy around one point does not imply homogeneity! Expansion of the Universe 6

9 World Models 8 9 Albert Einstein: Presence of mass leads to curvature of space (=gravitation) = General Theory of Relativity (GRT) GRT is applicable to Universe as a whole! A. Einstein ( ) Expansion of the Universe 7

10 World Models 8 9 Theoretical cosmology: Combination of 1. relativity theory A. Einstein ( ) Expansion of the Universe 8

11 World Models 8 9 Theoretical cosmology: Combination of 1. relativity theory 2. thermodynamics A. Einstein ( ) Expansion of the Universe 9

12 World Models 8 9 Theoretical cosmology: Combination of 1. relativity theory 2. thermodynamics 3. quantum mechanics A. Einstein ( ) Expansion of the Universe 10

13 World Models 8 9 Theoretical cosmology: Combination of 1. relativity theory 2. thermodynamics 3. quantum mechanics = complicated A. Einstein ( ) Expansion of the Universe 11

14 World Models 8 9 Theoretical cosmology: Combination of 1. relativity theory 2. thermodynamics 3. quantum mechanics = complicated A. Einstein ( ) Typically calculation performed in three steps: 1. Describe metric following the cosmological principle 2. Derive evolution equation from GRT 3. Use thermodynamics and quantum mechanics to obtain equation of state... and then do some maths Expansion of the Universe 12

15 World Models 8 10 A.A. Friedmann ( ) Friedmann: Mathematical description of the Universe using normal fixed coordinates ( comoving coordinates ), plus scale factor R which describes evolution of the Universe. Expansion of the Universe 13

16 World Models 8 10 R small R large Misner, Thorne, Wheeler Friedmann: Mathematical description of the Universe using normal fixed coordinates ( comoving coordinates ), plus scale factor R which describes evolution of the Universe. Expansion of the Universe 14

17 World Models 8 11 Using GR, derive equation for evolution of scale factor ( Friedmann equations ). Equations depend on World Model: Evolution of R as a function of time 1. Value of H as measured today (note: H is time dependent!) 2. Density of universe, Ω = Ω m + Ω Λ Density: universe evolves under its self gravitation, typically parameterised in units of critical density, ρ crit (density when universe will collapse in the future): Ω = ρ ρ crit where ρ crit = 3H2 0 8πG currently: ρ crit g cm 3 ( H-Atoms m 3 ). Total Ω is sum of: 1. Ω m : Matter, i.e., everything that leads to gravitative effects, Ω m in baryonic matter is 3% is baryonic, but note there might be nonbaryonic dark matter as well! 2. Ω Λ = Λc 2 /3H 2 : contribution caused by vacuum energy density Λ ( dark energy ) Expansion of the Universe 15

18 World Models 8 12 Omega<1, Lambda>0 no beginning, no end Lambda>0 Scale factor Exponentially expanding "steady state" univ Omega<1 big bang Omega>1 big bang and big crunch Omega=1 Lambda=0 Time today Many different kinds of world models are possible, behaviour of universe depends on Ω und Λ. Expansion of the Universe 16

19 3K CMB 8 13 I ν (W m 2 sr 1 Hz 1 ) Wavelength (cm) K blackbody FIRAS COBE satellite DMR COBE satellite UBC sounding rocket LBL-Italy White Mt. & South Pole Princeton ground & balloon Cyanogen optical Frequency (GHz) Penzias & Wilson (1965): Measurement of Excess Antenna Temperature at 4080 Mc/s = Cosmic Microwave Background radiation (CMB) CMB spectrum is blackbody with temperature T CMB = ± K. (Smoot et al., 1997, Fig. 1) Extrapolating CMB temperature back in time shows: Universe started with a hot big bang, has since cooled down. 3K CMB 1

20 World Models Perlmutter, Physics Today (2003) relative brightness expands forever collapses After inflation, the expansion either... first decelerated, then accelerated past...or always decelerated today future 10 redshift Billions Years from Today Note: Extrapolation backwards gives age of universe as roughly 1/H 0! for H 0 = 72 km s 1 Mpc 1 = s 1, giving an age of 13.6 Gyr. 3K CMB 2

21 History of the universe 8 15 R(t) t T[K] ρ matter Major Events since BB [K] [g cm 3 ] Planck era, begin of physics Inflation (IMPLIES Ω = 1) s generation of p-p, and baryon anti-baryon pairs from radiation background min generation of e -e + pairs out of radiation background min nucleosynthesis yr End of radiation dominated epoch yr Hydrogen recombines, decoupling of matter and radiation yr first stars formed yr now History of the universe 1

22 Conclusions 8 16 Modern Cosmology: Determination of H 0, Ω and Λ from observations and comparison with theory In the following: Examples for new measurements to determine Ω and Λ: Supernova observations and Cosmic Microwave Background (WMAP). General hope: confirmation that Ω m + Ω Λ = 1 as predicted by theory of inflation (this implies a flat universe). History of the universe 2

23 Supernovae Supernova Cosmology Project Knop et al. (2003) Ω Μ, Ω Λ 0.25, , 0 1, 0 effective m B Calan/Tololo & CfA Supernova Cosmology Project Supernova observations are well explained by models with Ω m = 0.25 and Ω Λ = redshift z Supernovae 1

24 Supernovae No Big Bang 68% 90% 95% 99% Ω Λ 1 0 expands forever recollapses eventually Supernova observations are well explained by models with Ω m = 0.25 and Ω Λ = Flat Λ = 0 Universe closed flat open Ω Λ = 0 is excluded by data! Ω Μ Supernovae 2

25 CMB, I 8 18 T=2.728K COBE (1992): First map of 3K-CMB T = K CMB 1

26 CMB, II 8 19 T=3.353mK Overlaid: Dipole anisotropy caused by motion of the solar system Temperature fluctuation: T/T 10 4 CMB 2

27 CMB, III 8 20 T=18 µ K At level of T/T 10 5 : Deviations from isotropy due to structure formation CMB 3

28 Wilkinson Microwave Anisotropy Probe (WMAP): Launch 2001 June 30, first publications 2003 February

29 Foreground features

30 WMAP, K-Band, λ = 13 mm, ν = 22.8 GHz, resolution 0.83

31 WMAP, Q-Band, λ = 7.3 mm, ν = 40.7 GHz, resolution 0.49

32 WMAP, W-Band, λ = 3.2 mm, ν = 93.5 GHz, resolution 0.21

33 Results 8 26 After Big Bang: universe dense ( foggy ), photons efficiently scatter off electrons = coupling of radiation and matter courtesy Wayne Hu Universe cools down: recombination of protons and electrons into hydrogen = no free electrons = scattering far less efficient = Photons: free streaming Photons escaping from overdense regions loose energy (gravitational red shift) = Observable as temperature fluctuation (Sachs Wolfe Effect) CMB Fluctuations Gravitational potential at z 1100 = structures CMB 9

34 Results 8 27 Strength of fluctuation large 1st acoustic peak Ω Λ Ω m h 2 Angular scale small (after Hu et al., 1995) Power spectrum of CMB depends on Ω m H 0 Ω Λ CMB 10

35 Results 8 27 Strength of fluctuation large 1st acoustic peak Ω Λ Ω m h 2 Angular scale small (after Hu et al., 1995) Power spectrum of CMB depends on WMAP best fit parameters (assuming Ω m H 0 Ω Λ Ω = 1, H 0 =: h 100 km s 1 Mpc 1 ): h = 0.72 ± 0.05 Ω m h 2 = 0.14 ± 0.02 CMB 11

36 Results Supernova Cosmology Project No Big Bang Knop et al. (2003) Spergel et al. (2003) Allen et al. (2002) Confidence regions for Ω Λ and Ω m. dark: 68% confidence, outer region: 90% 2 Ω = 1.02 ± 0.02 Ω Λ Clusters Supernovae CMB flat open expands forever recollapses eventually closed Ω m = H 0 = 72 ± 5 km s 1 Mpc 1 leading to an age of the universe of 13.7 billion years. This means: 70% of the universe is due to dark energy Ω M... and what this is: we have no clue CMB 12

37 Large Scale Structures dF Survey, galaxies total = structures Structure Formation 1

38 Large Scale Structures 8 30 We can use theories for nature of Λ and measured values of H 0 and Ω to predict how galaxies evolve in the universe. Virgo collaboration Structure Formation 2

39 Hubble Ultra Deep Field (11 days exposure!)

40 Hubble Ultra Deep Field (11 days exposure!)