Measurements of Cosmological ParametersAmedeo BalbiDipartimento di Fisica & INFNUniversità di Roma “Tor Vergata”

Background CosmologyExpanding universe, described by Friedmann equation:

20

2

2 3

1 Maa a a

H

-1 -10 100 km s Mpc

M

M B DM

h H

Perturbations & InflationInflation generates perturbations through amplification of quantum fluctuations. In the basic picture, they obey Gaussian statistics, with a Harrison-Zel’dovich power spectrum:

( ) nP k Ak

Parameters from the CMB

CMB Anisotropy

CMB Power Spectrum

Bennet et al. 2003

Total DensityThe typical angular size of fluctuations on the CMB depends on the global geometry of the Universe ( 1st peak position)

1.02 0.02

The universe is flat

Hubble ConstantHST Key Project: use Cepheids to calibrate distance indicators (z~0)Combining X-ray flux and SZ effect in clusters of galaxies (z~0.5)CMB: conformal distance to the decoupling surface (z~1000)

Spergel et al. 2003

Cosmic Ages

Spergel et al. 2003

Baryon AbundanceCMB, ratio of acoustic peaks amplitude (Spergel et al. 2003):

Primordial abundance of deuterium + BBN (Fields & Sarkar, 2004):

2 0.024 0.001Bh

20.012 0.025 (95% CL)Bh

Primordial Abundances

Fields & Sarkar, 2004

Matter DensityPower spectrum from redshift surveys (e.g., 2dF, SDSS):

0.6

0.18 0.020.17 0.06

0.49 0.09( 1)

M

B M

M

h

bb

Clusters of galaxies (e.g., Chandra):

0.3BB M

M

f

Something Missing!

1 0.3M

Type Ia Supernovae

20 0

1 12LH d z q z

00 2

0

02Maq

a

0.7

Cosmic Concordance

M 1

(CMB)1/3

(LSS)2/3(SN)

Amplitude of fluctuations

Spergel et al. 2003

InflationUniverse is flatPrimordial perturbations are adiabatic, Gaussian and scale-invariant (spectral index near unity)Gravitational wave background (tensor modes) is negligible

No viable alternative makes all these predictions

Problems with LambdaVacuum fluctuations in QFT:

40 12010 10 “Why now?”:

3 when 1Ma a

Dark Energy?Ideal fluid with generic equation of state:

( )1 3

w a pw

E.g., scalar field:2

2

2 ( )

2 ( )

V

p V

Constraints on Dark Energy

Seljak et al. 2004

Precision Cosmology