Introduction to Cosmology

1. Introduction to Cosmology Josh Frieman Structure Evolution & Cosmology, Santiago, Oct. 2002

2. Evolution of the Universe Important to distinguish: 1. What we `know’ (well-established by observations): The Standard Cosmology 2. Speculations/theories that extend beyond the well-established and attempt to explain otherwise unexplained phenomena.

3. The Big Bang Theory:well-tested framework for understanding the observationsand for asking new questions Universe expanding isotropically from a hot, dense `beginning’ (aka the Big Bang) about 14 billion years ago The only successful framework we have for explaining several key facts about the Universe: Hubble’s law of galaxy recession: expansion Uniformity (isotropy) of Microwave background Cosmic abundances of the light elements: Hydrogen, Helium, Deuterium, Lithium, cooked in the first 3 minutes Formation of Large-scale Structure

4. The Big Bang Theory: Status A useful idealization, a simplified description analogous to the approximation of the Earth as a sphere Even so, basic elements of the model remain to be understood: e.g., the natures of the Dark Matter & Dark Energy which together make up 95% of the mass-energy of the Universe These puzzles do NOT mean that the Big Bang Theory is wrong—rather, it provides the framework for investigating them.

6. Hubble’s Law and the Expanding Universe Slipher (1922): measured redshifts (recession velocities v) of 40 spiral galaxies by their spectra: Doppler effect Henrietta Leavitt: studied Cepheid variable stars in our Galaxy, showed a correlation between their Luminosity and their Period of variation: L() Hubble (1929):found Cepheids in ~20 nearby galaxies and measured their periods  inferred L. From their apparent brightness (flux f = L/4πd2), he obtained their distances d. Comparing the distances d with Slipher’s radial velocities v, he empirically found that v=H0d where H0=550 km/sec/Megaparsec = Hubble’s constant

7. We observe Hubble law: vB=HdB vA=HdA By vector addition, vBA=vB-vA =H(dB-dA) =HdBA Observer A sees Galaxy B recede according to the Hubble Law as well: Hubble (linear) Law is Universal D B vBA vD vB vA A Us v2 vC C

8. `Doppler’ shift of Galaxy Emission/Abs. Lines v/c ≈ z = /0 (approximation for objects moving with v/c << 1) receding slowly  receding quickly

9. SDSS QSOs

10. Hubble Space Telescope

11. Hubble Space Telescope image 40 Cepheids

13. v = H0d + vpec Hubble (1929) Hubble Space Telescope (2000) Freedman, etal

14. Hubble Diagram extended to larger distances using objects brighter than Cepheids Modern Value: H0 = 72  8 km/sec/Mpc

15. Spectrum of the Cosmic Microwave Background Radiation (1965) Photon energy measured by the COBE satellite (1990): no deviations from Blackbody spectrum yet observed

16. The Microwave Sky: The Universe is filled with relic thermal radiation: Cosmic Microwave Background (CMB) COBE Map of the Temperature of the Universe On large scales, the Universe is (nearly) isotropic around us (the same in all directions): CMB radiation probes as deeply as we can, far beyond optical light from galaxies: snapshot of the young Universe: t = 400,000 years (z = 1000) recombination T = 2.728 K Scale of the Observable Universe: Size ~ 1028 cm Mass ~ 1023 Msun

18. The Microwave Sky: COBE Map of the Temperature of the Universe Dipole anisotropy due to our Galaxy’s peculiar motion through the Universe T = 2.728 K Red: 2.7+0.003 Blue:2.7-0.003 Red: 2.7+0.00001 deg Blue: 2.7-0.00001 deg

19. The Microwave Sky: COBE Map of the Temperature of the Universe Map with Dipole anisotropy removed: fluctuations of the density of the Universe plus Galactic emission T = 2.728 K Red: 2.7+0.003 Blue:2.7-0.003 Red: 2.7+0.00003 deg Blue: 2.7-0.00003 deg

20. The Cosmological Principle A working hypothesis (aka the Copernican Principle): We are not priviledged observers at a special place in the Universe: At any instant of time, the Universe should appear ISOTROPIC (over large scales) to All observers. A Universe that appears isotropic to all observers is HOMOGENEOUS i.e., the same at every location (averaged over large scales).

21. Statistical homogeneity

22. Homogeneity & Isotropy: Universe described by single degree of freedom a(t)

23. 2-D Analogue radius a(t1): Cosmic Scale Factor On average, galaxies are at rest in these expanding (comoving) coordinates radius a(t2)

24. Features of the Expansion of the Universe: • Galaxies and Clusters of galaxies are not expanding • with the Universe: they are gravitationally bound systems. • New interpretation of the Redshift of Light: • wavelength of light (and all radiation) stretches with expansion: • wavelength (t) proportional to scale factor a(t) • energy E(t) inverselyproportional to a(t) • where a(t) is the Cosmic Scale Factor (“radius”) • Redshift: 1+z = a(t0)/a(te) t0 = age of U today • te= age when light • was emitted

25. The Redshift Redshift: 1+z = a(t0)/a(te) t0 = age of U today =(t0)/ (te) te = age when light was emitted This expression holds in general, replacing the Doppler formula which held for velocities v << c. No need to talk about recession velocities of galaxies, since they are at rest in the system of expanding coordinates (except for peculiar velocities). (In particular, objects with redshifts z > 1 are not moving faster than the speed of light!)

26. `Newtonian’ Cosmology How does the `size’ (scale factor) a(t) of the Universe evolve? Consider a homogenous ball of matter (Birkhoff): Kinetic Energy mv2/2 Gravitational Potential Energy -GMm/d (Newton) Conservation of Energy: Kinetic + Potential = Total E = constant mv2/2- GMm/d= E Now use v=Hd (Hubble) and M=V=(4/3)d3 to find H2 - (8/3)G = 2E/md2 = -k/a2 where H= Hubble parameter = expansion rate (H quantifies time rate of change of a(t)) M d  a m d density of Universe Friedmann equation

27. Einstein Cosmology H2 (da/dt)2/a2 = (8/3)G  k/a2 Friedmann Expansion rate Spatial curvature Scale factor Define the critical density:crit = 3H02/8G  1.9h2x10-29 grams/cm3 and the density parameter:0 = /critm ~ a-3 rad ~ a-4 0 > 1 implies k>0 positive spatial curvature 0 = 1 implies k=0 flat 0 < 1 implies k<0 neg. curvature 1 - 0 = -k/a02H02

28. Einstein: space can be globally curved k = +1 k = -1 k = 0 What is the geometry of three-dimensional space?

29. Physical Implications of Expanding Universe An expanding gas cools (TCMB ~ 1/a(t)) and becomes less dense (n ~ 1/a3(t)) as it expands. Run the expansion backward: going back into the past, the Universe heats up and becomes denser. Expanding Universe plus known laws of physics imply the Universe has finite age and a nearly `singular’ (infinite density and Temperature) beginning about 14 Billion years ago: THE BIG BANG

30. The Hot Big Bang: relics from the Early Universe How do we test the idea that the early Universe was very hot? Look for relics of this hot phase, observable signatures that require high Temperature (and density) to produce. Best-established signatures: --Cosmic Microwave Background Radiation (CMB) --Abundances of the Light Elements Additional signatures of the Early Universe: --Dark matter particles --Primordial density perturbations which produced CMB anisotropies and (later) galaxies & Large-scale structure --The baryon asymmetry --Topological defects

31. Relics produced when their interactions drop out of Thermodynamic Equilibrium: int/H < 1 Dark matter freeze-out See talk by Binetruy

32. Big Bang Nucleosynthesis Origin of the Light Elements: Helium, Deuterium, Lithium,… When t < 1 minute, T > 109 K, atomic nuclei could not survive: the baryons formed a soup of protons & neutrons. As the Temperature dropped below this value (set by the binding energy of light nuclei), protons and neutrons began to fuse together to form bound nuclei:the light elements were synthesized as the Universe expanded and cooled. t(sec) = (kT/MeV)2during radiation era

33. Light Element Abundances: predictions Early Universe: protons, neutrons, electrons, neutrinos, photons. Stage 1: t < 1 sec, kT > 1 MeV: Weak interactions interconvert neutrons & protons: n  p+e+ In equilibrium, n/p = exp((mn-mp)c2/kT). At t ~ 1 sec, weak interactions freeze out (wk/H < 1), leaving (n/p)F = 1/6. Later, this ratio falls much more slowly due to neutron decay.

34. Abundance predictions Stage 2: t ~ 1 minute, T ~ 100 keV Neutrons and protons fuse to Deuterium (1 neutron+1 proton), Tritium (1p,2n), Helium4 (2n,2p), and Lithium7 (3p, 4n). Heavier nuclei not produced due to absence of stable mass 5 and 8 elements. By this time, due to neutron decay, n/p ~ 1/7. He4 is the most stable (most strongly bound) light nucleus, so essentially all the available neutrons end up in He4 He4 mass fraction Y~ 2n/(n+p) ~ 0.25 25% of the baryonic mass is in Helium, essentially all the rest in Hydrogen, and trace amounts in Deuterium and Lithium.

35. BBN predicted abundances h = H0/(100 km/sec/Mpc) Fraction of baryonic mass in He4 Light Element abundances depend mainly on the density of baryons in the Universe Deuterium to Hydrogen ratio Lithium to Hydrogen ratio baryon/photon ratio

36. BBN Theory vs. Observations: Observational constraints shown as boxes Remarkable agreement over 10 orders of magnitude in abundance variation Concordance region: b h2 = 0.02  0.001 For h=0.7, this implies b = 0.04. Strongest constraint comes from Deuterium (QSO absorption lines) b 4He

37. BBN & the Baryon Density Light element abundances are concordant if the baryon (neutron+proton) to photon ratio is about  = nb/nphoton= 6 x 10-10 or bh2= 0.02 (We can make the conversion from  to b h2since we know the present density of CMB photons, nphoton = 420 per cm3, very precisely from the CMB Temperature.) This determination is in excellent agreement with the amplitude of the `acoustic peaks’ in the CMB temperature anisotropy announced last year.

38. Structure as a Cosmological Probe Paradigm for Structure Formation (SF): Nearly scale-invariant primordial, adiabatic perturbations from inflation, amplified by gravity, in a Universe with (nearly) cold dark matter. While understanding galaxy formation in detail remains difficult (see talk by Silk), the SF paradigm appears robust: confirmed by Large-scale Structure (LSS) and CMB observations. As a result, CMB and LSS now providing sensitive new probes of cosmological parameters.

39. Recent CMB experiments: Going to smaller angular scales  higher resolution

40. Recent CMB Anisotropy Experiments: South Pole Boomerang DASI

41. CMB Angular Power Spectrum Statistical way to characterize the spatial structure in a 2-dimensional image or map T/T =  alm Ylm(,) Cl = <|alm|2> Power spectrum Power spectrum contains all the information if the image is Gaussian

45. Physics of CMB Anisotropy • Acoustic oscillations of the • Photon-baryon fluid when the • Universe was 400,000 yrs old • Imprint on the Microwave sky Hu

46. Theoretical dependence of CMB anisotropy on the baryon density Angular frequency Angular separation on the sky

47. Microwave Background AnisotropyProbesWb(Baryon Density) Boomerang experiment (2001) Wbh2= 0.0220.002 DASI experiment (2001)

48. Microwave photons traverse a significant fraction of the Universe, so they can probe its spatial curvature Sizes of hot and cold spots in the CMB give information on curvature of space: In curved space, light bends as it travels: fixed object has larger angular size in a positively curved space: CMB spots appear larger. Opposite occurs for negatively curved space.

50. Position of first Peak probes the spatial Curvature of the Universe