cosmology: an introduction - kiasconf.kias.re.kr/~brane/wc2012/download/introduction to...cosmology...

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, …


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 5Cosmology EJChun@KIAS

I. The accelerating Universe


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:


Two dimensional example

• Two sphere, S2 :



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

• Volume of the two sphere (positive curvature):



• H2 (negative curvature): a i a

• E2 (flat):


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).


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:


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).



• 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:



• 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


Hubble’s Law

• The change of the scale factor around t0:

• Hubble parameter:• Deceleration parameter:


Hubble’s Law

• Geodesic equation relates r1 and z:

• which leads to the Hubble’s law:

Note:


1929


Hubble Wilson observatory

1998


SupernovaCosmology Project (SCP)

High-z SupernovaSearch Team (HST)

II. Friedmann-Lemaitre Universe


“His greatest blunder”

Einstein Universe 1917

Big Bang

1922

1927


“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:


Units

• Hubble constant:

• Hubble time/distance:

• CMB temperature:


General relativity

• Newtonian gravity:

gravitational force mass

• Einstein gravity:

curved spacetime energy-momentum


Note) Electromagnetism

General relativity

• Metric:• Connection:• Riemann tensor:

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


(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):


Friedmann equations

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

• Energy-momentum tensor components:


Friedmann equations

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

• Hubble parameter and critical density:


Evolution of energy density

• Energy-momentum conservation:

• Equation of state:

• When the Universe is dominated by one type:


Evolution of energy density


Expansion of the Universe

• Deceleration parameter:


Age of the Universe

• Express a & H in terms of z:

• Integrate dt=da/aH:


Luminosity distance

• Full expression (k=0):

• For small z:


Horizon size

• The proper distance to the horizon:

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


Horizon problem

• Comoving coordinate of horizon at t:


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:


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.


2003


“From speculation to precision”


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


ΛCDM Model

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.


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


Thermal distributions

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

• Integrating out the angular distributions:


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),


Radiation energy density

• The energy density including only relativistic particles: ρR

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


Radiation dominated era

• At earlier time when ρ=ρR, a~t1/2 :


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.


IV. Thermal history of the Universe


Today

• Photon (CMB) density:

• Entropy density:

• Critical density:


Today

• Baryon number density:

• Radiation fraction:


Radiation-Matter equality

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


Birth of CMBR

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


Nucleosynthesis

The αβγ paper


Dark Matter Genesis

Out of equilibrium when relativistic(HDM)

In thermal equilibrium

Out of equilibriumwhen non-relativistic(CDM) WIMP


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?


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)?


cosmology: an introduction - kiasconf.kias.re.kr/~brane/wc2012/download/introduction to...cosmology...

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