#
waynehu

## Professor,
Department of Astronomy and Astrophysics

University of Chicago

# Power Spectrum

Accurate theoretical anisotropy power spectra for popular
models have long been available and codes to calculate them are now fast and public (e.g.
Seljak & Zaldarriaga
1996). Here we will concentrate on the gross features of the spectrum
which are likely to occur in most models.

The physical scales associated with the acoustic
(A), matter-radiation equality (eq), damping
(D),and late ISW (KLambda) anisotropy formation
mechanisms are imprinted on the anisotropy power spectrum.

*Figure: *Cosmological Parameter
Dependence

A scale-invariant adiabatic example. Power spectrum of temperature anisotropies
in multipole space (*l *is proportional to the inverse of the angle).
Independent of these *scalar* effects, there may be tensor
contributions below the acoustic scale in *l *.

The exact dependence of the anisotropies on these scales depends on
the model for structure formation through the
potential envelope that governs ISW and acoustic
effects. Nevertheless, these four physical scales are generically imprinted
on the CMB unless secondary anisotropies,
e.g. from reionization dominate. Once
measured, these four scales can be combined to extract four fundamental
cosmological parameters in a robust fashion: the curvature, cosmological
constant, matter-radiation ratio (Omega_0 h^2), and baryon-photon ratio
(baryon content Omega_B h^2). Furthermore consistency checks can be made
with some model assumptions. In adiabatic models,
baryon drag provides another measure of the baryon content through the
alternating peak heights and the shape of the large scale structure power
spectrum checks the inferred matter-radiation ratio.