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.

2012 Winter camp Cosmology EJChun@KIAS 2

Ref.) Kolb and Turner (1988)

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, …

2012 Winter camp Cosmology EJChun@KIAS 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

2012 Winter camp Cosmology EJChun@KIAS 4

2012 Winter camp 5Cosmology EJChun@KIAS

I. The accelerating Universe

2012 Winter camp 6Cosmology EJChun@KIAS

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 UniverseRobertson-Walker (RW) metric:

2012 Winter camp 7Cosmology EJChun@KIAS

Two dimensional example

• Two sphere, S2 :

2012 Winter camp 8Cosmology EJChun@KIAS

Two dimensional example

• In terms of the usual polar and azimuthalangles of spherical coordinates:

• Volume of the two sphere (positive curvature):

2012 Winter camp 9Cosmology EJChun@KIAS

Two dimensional example

• H2 (negative curvature): a i a

• E2 (flat):

2012 Winter camp 10Cosmology EJChun@KIAS

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).

2012 Winter camp 11Cosmology EJChun@KIAS

Horizon distance

• Light travels along geodesics:• A light signal emitted at (rH,θ0,φ0) at t reaches

at (0,θ0,φ0) at t=0:

• The proper distance to the horizon measured at time t:

2012 Winter camp 12Cosmology EJChun@KIAS

Red-shift and luminosity distance

• The wavelength at present t0 differs from that at an earlier time t1:

• In the expanding Universe, a light signal from a more distant source is more red-shifted(larger z).

2012 Winter camp 13Cosmology EJChun@KIAS

Red-shift and luminosity distance

• A wave emitted at time t1 at comovingcoordinate r1 arrives at a detector now (t0) at r=0:

• The wavecrest emitted at t1+δt1 arrives at the detector at t0+δt0:

2012 Winter camp 14Cosmology EJChun@KIAS

Red-shift and luminosity distance

• Suppose a source with an absolute luminosity L (the energy per time) emitting light at t1. Its luminosity distance is defined by its measured flux F (the energy per time per area) at present:

• If a source at comoving coordinate r1 emits light at t1and a detector at r=0 detects it at t0, the total energy measured now is

2012 Winter camp 15Cosmology EJChun@KIAS

Hubble’s Law

• The change of the scale factor around t0:

• Hubble parameter:• Deceleration parameter:

2012 Winter camp 16Cosmology EJChun@KIAS

Hubble’s Law

• Geodesic equation relates r1 and z:

• which leads to the Hubble’s law:

Note:

2012 Winter camp 17Cosmology EJChun@KIAS

1929

2012 Winter camp 18Cosmology EJChun@KIAS

Hubble Wilson observatory

1998

2012 Winter camp 19Cosmology EJChun@KIAS

SupernovaCosmology Project (SCP)

High-z SupernovaSearch Team (HST)

2012 Winter camp 20Cosmology EJChun@KIAS

II. Friedmann-Lemaitre Universe

2012 Winter camp 21Cosmology EJChun@KIAS

“His greatest blunder”

Einstein Universe 1917

Big Bang

1922

1927

2012 Winter camp 22Cosmology EJChun@KIAS

“Big Bang--pseudoscience”, Hoyle

“a brilliant solution”, Edington

Forgotten pioneer, died 1925

1929 Hubble

Units

• Natural unit: [Energy]=[Mass]=[Temperature]=[Length]-1=[Time]

• Reduced Planck mass:

• Fermi constant:

2012 Winter camp 23Cosmology EJChun@KIAS

Units

• Hubble constant:

• Hubble time/distance:

• CMB temperature:

2012 Winter camp 24Cosmology EJChun@KIAS

General relativity

• Newtonian gravity:

gravitational force mass

• Einstein gravity:

curved spacetime energy-momentum

2012 Winter camp 25Cosmology EJChun@KIAS

Note) Electromagnetism

General relativity

• Metric:• Connection:• Riemann tensor:

• Ricci tensor:• Ricci scalar:• Einstein equation:

2012 Winter camp 26Cosmology EJChun@KIAS

(Tμν contains Λ or DE)

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):

2012 Winter camp 27Cosmology EJChun@KIAS

Friedmann equations

• Non-zero components of the Ricci tensor and scalar:

• Energy-momentum tensor components:

2012 Winter camp 28Cosmology EJChun@KIAS

Friedmann equations

• Dynamics of a(t) determined by ρ(t) and p(t):

• Hubble parameter and critical density:

2012 Winter camp 29Cosmology EJChun@KIAS

Evolution of energy density

• Energy-momentum conservation:

• Equation of state:

• When the Universe is dominated by one type:

2012 Winter camp 30Cosmology EJChun@KIAS

Evolution of energy density

2012 Winter camp Cosmology EJChun@KIAS 31

Expansion of the Universe

• Deceleration parameter:

2012 Winter camp 32Cosmology EJChun@KIAS

Age of the Universe

• Express a & H in terms of z:

• Integrate dt=da/aH:

2012 Winter camp 33Cosmology EJChun@KIAS

Luminosity distance

• Full expression (k=0):

• For small z:

2012 Winter camp Cosmology EJChun@KIAS 34

Horizon size

• The proper distance to the horizon:

• The size of the horizon today at the Planck time (a rough estimate assuming RD):

2012 Winter camp 35Cosmology EJChun@KIAS

Horizon problem

• Comoving coordinate of horizon at t:

2012 Winter camp 36Cosmology EJChun@KIAS

Flatness problem

• At present, Ω0~1 Rcurv~H0-1 and ρ0∼ρc

• At earlier time, radiation dominates (ρ ∝ 1/a4):

• At Planck time, initial data must be arranged in a very special way:

2012 Winter camp 37Cosmology EJChun@KIAS

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.

2012 Winter camp Cosmology EJChun@KIAS 38

2003

2012 Winter camp Cosmology EJChun@KIAS 39

“From speculation to precision”

2012 Winter camp Cosmology EJChun@KIAS 40

Balckbody radiationwith T=2.728K

∆T/T ~ 10-5

2006 Nobel

Standard Cosmological Model

Dark energy: 73%Matter: 27%

Dark matter: 22.7%Atom: 4.55%

Neutrino: 0.1-1%Radiation: 0.005%

t0=13.73 GyrH0=70.2 km/sec/Mpc

2012 Winter camp 41Cosmology EJChun@KIAS

ΛCDM Model

2012 Winter camp 42Cosmology EJChun@KIAS

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.

2012 Winter camp 43Cosmology EJChun@KIAS

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

2012 Winter camp Cosmology EJChun@KIAS 44

Thermal distributions

• The number density, energy density, and pressure of an ideal gas of particles are

• Integrating out the angular distributions:

2012 Winter camp Cosmology EJChun@KIAS 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),

2012 Winter camp Cosmology EJChun@KIAS 46

Radiation energy density

• The energy density including only relativistic particles: ρR

• Total number of relativistic (massless) degrees of freedom: g*

2012 Winter camp Cosmology EJChun@KIAS 47

Radiation dominated era

• At earlier time when ρ=ρR, a~t1/2 :

2012 Winter camp Cosmology EJChun@KIAS 48

Entropy

• Entropy density:

• Conservation of the entropy of the Universe:

• The number of a particle in a comovingvolume:

• It remains constant if a particle is not being created or destroyed.

2012 Winter camp Cosmology EJChun@KIAS 49

2012 Winter camp 50Cosmology EJChun@KIAS

IV. Thermal history of the Universe

2012 Winter camp Cosmology EJChun@KIAS 51

Today

• Photon (CMB) density:

• Entropy density:

• Critical density:

2012 Winter camp Cosmology EJChun@KIAS 52

Today

• Baryon number density:

• Radiation fraction:

2012 Winter camp Cosmology EJChun@KIAS 53

Radiation-Matter equality

• Recalling ρm/ρr~a, we get ρm = ρr at

2012 Winter camp Cosmology EJChun@KIAS 54

Birth of CMBR

• Photon goes out of thermal equilibrium at 1+zdec when the reaction rate for is smaller than the expansion rate.

2012 Winter camp Cosmology EJChun@KIAS 55

Nucleosynthesis

The αβγ paper

2012 Winter camp 56Cosmology EJChun@KIAS

Dark Matter Genesis

Out of equilibrium when relativistic(HDM)

In thermal equilibrium

Out of equilibriumwhen non-relativistic(CDM) WIMP

2012 Winter camp 57Cosmology EJChun@KIAS

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?

2012 Winter camp Cosmology EJChun@KIAS 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)?

2012 Winter camp Cosmology EJChun@KIAS 59