Theory ofCosmological Perturbations

Misao Sasaki

YITP, Kyoto University

preliminary

• 1916~ GR cosmological models

• 1929 Hubble’s law

• 1946~ Big-bang model

• 1965 Discovery of CMB

• 1980~ Revelation of Large Scale Structure

Birth of Particle Cosmology

• 1992 Detection of CMB Anisotropy

• 2003 Existence of Dark Energy

• 2013 Strong Evidence for Inflation

• 21st Century Era of Precision Cosmology

Progress in Cosmology

1Gly

2Gly

Large Scale Structure

44

CMB spectrum at T=2.725K

(redshifted by 103 from LSS)

wavelength[mm]

frequency[GHz]

200 sigma

error-bars

COBE/FIRAS (’94)

CMB spectrum by COBE

isotropic component =2.73 KCMBT

CMB Full Sky Map

5

-5

2 70010( / )CMBT T

COBE-DMR (1990)

WMAP (2003~)

Planck (2013~) WMAP 7th year data

Planck 2013

-5

2010 Large Scale Structure( / )CMBT T

strong evidence for inflation

highly Gaussian fluctuations

almost scale-invariant spectrum

1 2

0

( ) ( )

2 1 (cos ).

4

T

C

T n n

P

CMB angular power spectrum

Planck 2013

Cosmic Thermal History & Hubble Horizon

n-decoupling:

nucleosynthesis

baryogenesis? baryon-photon

decoupling:

last scattering surface

now

Hubble

horizon

2 2 2 2 2 2 2 ds dt a t dx a d dx

0

t dt

a(t )

Horizon Problem

Evolution of Inhomogeneities

• evolution on scales greater than Hubble horizon

•

• general relativistic treatment is mandatory

3 3

2 2

22

2

2

4 2 8

3 3

8

3

g

g

H H

r fo H

GM GM r r r r

c c

G c rH r r r

r rr r

general relativistic cosmological perturbation theory

“gravitational” radius > r >Hubble radius

selected references

basics on cosmological perturbations

• H. Kodama and M. Sasaki

Cosmological Perturbation Theory

Prog. Theor. Phys. Suppl. 78 (1984) 1-166.

very good textbook on early universe cosmology including inflation

• V. Mukhanov,

Physical foundations of cosmology

Cambridge, UK: Univ. Pr. (2005)

classic textbook on quantum field in curved spacetime

• N.D. Birrell and P.C.W. Davies

Quantum Fields in Curved Space

Cambridge Mongr. Math. Phys. (1982)