Cosmology: An Introduction Eung Jin Chun
Cosmology Hot Big Bang + Inflation. Theory of the evolution of the Universe described by General relativity (spacetime) Thermodynamics, Particle/nuclear physics (matter/energy contents), Astrophysics at large scale. Ref.) Kolb and Turner (1988) 2
Observational breakthrough Expanding Universe: Hubble 1929 Cosmic microwave background radiation: Penzias & Wilson 1964 Primary temperature anisotropy: COBE (Smoot, Mather) 1992 Accelerating Universe: Perlmutter, Schmidt- Riess 1998 Standard Model of Cosmology: WMAP (and SCP, 2dF GRS, SDSS) 2003 The future? PLANCK, SNAP, 3
Theoretical ideas and tools Universe equation: Einstein 1917 Expanding Universe: Friedman, Lemaitre 1920s Big Bang Nucleosynthesis (hot Universe): Alpher, Gamow, Herman 1940s Structure formation from primordial density perturbation: Harrison, Zel dovich 1970s Inflation: Guth 1980, Sato 1981 Cosmological perturbation theory: Bardeen, Kodama-Sasaki, 1980s 4
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I. The accelerating Universe 6
Spacetime geometry of the Universe The distribution of matter and radiation in the observable Universe is homogeneous and isotropic at large scale. Homogeneous and isotropic Universe Robertson-Walker (RW) metric: 7
Two dimensional example Two sphere, S 2 : 8
Two dimensional example In terms of the usual polar and azimuthal angles of spherical coordinates: Volume of the two sphere (positive curvature): 9
Two dimensional example H 2 (negative curvature): a ia E 2 (flat): 10
Robertson-Walker metric The scale factor a(t) determines the length scale (the size of the universe) at a given t: (r, θ, φ) : comoving coordinates. Dynamics (history) of the Universe dictated by the solution of the one variable a(t). 11
Horizon distance Light travels along geodesics: A light signal emitted at (r H,θ 0,φ 0 ) at t reaches at (0,θ 0,φ 0 ) at t=0: The proper distance to the horizon measured at time t: 12
Red-shift and luminosity distance The wavelength at present t 0 differs from that at an earlier time t 1 : In the expanding Universe, a light signal from a more distant source is more red-shifted (larger z). 13
Red-shift and luminosity distance A wave emitted at time t 1 at comoving coordinate r 1 arrives at a detector now (t 0 ) at r=0: The wavecrest emitted at t 1 +δt 1 arrives at the detector at t 0 +δt 0 : 14
Red-shift and luminosity distance Suppose a source with an absolute luminosity L (the energy per time) emitting light at t 1. Its luminosity distance is defined by its measured flux F (the energy per time per area) at present: If a source at comoving coordinate r 1 emits light at t 1 and a detector at r=0 detects it at t 0, the total energy measured now is 15
Hubble s Law The change of the scale factor around t 0 : Hubble parameter: Deceleration parameter: 16
Hubble s Law Geodesic equation relates r 1 and z: which leads to the Hubble s law: Note: 17
1929 Hubble Wilson observatory 18
1998 Supernova Cosmology Project (SCP) High-z Supernova Search Team (HST) 19
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II. Friedmann-Lemaitre Universe Einstein Universe 1917 His greatest blunder 21
Big Bang 1922 Forgotten pioneer, died 1925 1927 a brilliant solution, Edington Big Bang--pseudoscience, Hoyle 1929 Hubble 22
Units Natural unit: [Energy]=[Mass]=[Temperature]=[Length] -1 =[Time] Reduced Planck mass: Fermi constant: 23
Units Hubble constant: Hubble time/distance: CMB temperature: 24
General relativity Newtonian gravity: gravitational force mass Einstein gravity: curved spacetime energymomentum Note) Electromagnetism 25
General relativity Metric: Connection: Riemann tensor: Ricci tensor: Ricci scalar: Einstein equation: (T μν contains Λ or DE) 26
Friedmann equations Homogeneous and isotropic universe Robertson-Walker metric: Energy-momentum of a perfect fluid characterized by an energy density ρ(t) and pressure p(t): 27
Friedmann equations Non-zero components of the Ricci tensor and scalar: Energy-momentum tensor components: 28
Friedmann equations Dynamics of a(t) determined by ρ(t) and p(t): Hubble parameter and critical density: 29
Evolution of energy density Energy-momentum conservation: Equation of state: When the Universe is dominated by one type: 30
Evolution of energy density 31
Expansion of the Universe Deceleration parameter: 32
Age of the Universe Express a & H in terms of z: Integrate dt=da/ah: 33
Luminosity distance Full expression (k=0): For small z: 34
Horizon size The proper distance to the horizon: The size of the horizon today at the Planck time (a rough estimate assuming RD): 35
Horizon problem Comoving coordinate of horizon at t: 36
Flatness problem At present, Ω 0 ~1 R curv ~H 0-1 and ρ 0 ρ c At earlier time, radiation dominates (ρ 1/a 4 ): At Planck time, initial data must be arranged in a very special way: 37
Inflation Solves the horizon and flatness problems predicting Ω=1. Quantum fluctuation frozen to produce a small density perturbation which evolves to produce temperature anisotropy and large scale structure formation. 38
2003 39
From speculation to precision 2006 Nobel Balckbody radiation with T=2.728K T/T ~ 10-5 40
Standard Cosmological Model t 0 =13.73 Gyr H 0 =70.2 km/sec/mpc ΛCDM Model Dark energy: 73% Matter: 27% Dark matter: 22.7% Atom: 4.55% Neutrino: 0.1-1% Radiation: 0.005% 41
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III. Hot Big Bang Today the Universe has the background radiation of 2.73K microwave photons (CMBR). At earlier time, the Universe was denser and hotter, and there were other relativistic particles in thermal equilibrium. 43
Equilibrium thermodynamics A particle in kinetic equilibrium has the phase space distribution [+1 FD; -1 BE]: In chemical equilibrium of the particles, their chemical potentials are related. If they interact by the process A+B C+D, we get 44
Thermal distributions The number density, energy density, and pressure of an ideal gas of particles are Integrating out the angular distributions: 45
Thermal distributions In the relativistic limit (T>>m) (assume μ=0 from now on), for a (fermion) boson, In the non-relativistic limit (T<<m), 46
Radiation energy density The energy density including only relativistic particles: ρ R Total number of relativistic (massless) degrees of freedom: g * 47
Radiation dominated era At earlier time when ρ=ρ R, a~t 1/2 : 48
Entropy Entropy density: Conservation of the entropy of the Universe: The number of a particle in a comoving volume: It remains constant if a particle is not being created or destroyed. 49
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IV. Thermal history of the Universe 51
Today Photon (CMB) density: Entropy density: Critical density: 52
Today Baryon number density: Radiation fraction: 53
Radiation-Matter equality Recalling ρ m /ρ r ~a, we get ρ m = ρ r at 54
Birth of CMBR Photon goes out of thermal equilibrium at 1+z dec when the reaction rate for is smaller than the expansion rate. 55
Nucleosynthesis The αβγ paper 56
Dark Matter Genesis In thermal equilibrium Out of equilibrium when relativistic (HDM) Out of equilibrium when non-relativistic (CDM) WIMP 57
Baryogenesis At an early universe with a high temperature, #matter=#antimatter: Today, the Universe contains only matter: e - and baryons (p,n). What happened to their anti-particles (e +, anti-baryons)? Generation of baryon asymmetry? 58
Open questions Is there an origin of big-bang? What drives inflation? What is the origin of matter-antimatter asymmetry? What is dark energy (c.c., quintessense, )? What is the identity of dark matter? Can we understand the structure formation at smaller scales (baryon and DM distribution)? 59