University of Chicago

- Review Home
- Introduction
- Observables
- Acoustic Peaks
- Matter Power Spectrum
- Gravitational Secondaries
- Scattering Secondaries
- Non-Gaussianity
- Data Analysis
- Discussion

Standard Cosmological Paradigm

While a review of the standard cosmological paradigm is not our intention (see [Narkilar & Padmanabhan, 2001] for a critical appraisal), we briefly introduce the observables necessary to parameterize it.

The expansion of the Universe is described by the scale
factor *a*(*t*), set to unity today, and by the current expansion rate, the Hubble
constant
*H*_{0}=100*h* km/s/Mpc
with
*h*~0.7 [Freedman et al, 2001]. The Universe is
*flat* (no spatial curvature) if the total density is equal to the
critical density,
&rho_{c}=1.88*h*^{2}x 10^{-29}
g/cm^{3}; it is *open* (negative curvature)
if the density is less than this and *closed*
(positive curvature) if greater. The mean densities
of different components of the Universe control *a*(*t*)
and are typically expressed today in units of the critical density
&Omega_{i}, with an evolution with
*a*(*t*)
specified by equations of state
*w*_{i}=
*p*_{i}/&rho_{i},
where
*p*_{i}
is the pressure of the *i*th
component. Density fluctuations are determined by these parameters
through the gravitational instability of an
initial spectrum of fluctuations.

The
working cosmological model
contains
photons ,
neutrinos ,
baryons ,
cold dark matter ,
and
dark energy with densities proscribed
within a relatively tight range. For the radiation,
&Omega_{r}=4.17x10^{-5}*h*^{-2}
(*w*_{r}=1/3).
The photon contribution to the radiation is determined to
high precision by the measured CMB temperature,
*T*=2.728±0.004K
[Fixsen et al, 1996]. The neutrino contribution
follows from the assumption of 3 neutrino species, a standard thermal history,
and a negligible mass *m*_{&nu} <<1eV.
Massive neutrinos have an equation of state
*w*_{&nu}=1/3→0
as the particles become non-relativistic.
For
*m*_{&nu}~1eV
this occurs at
*a*~10^{-3}
and can leave a small but potentially measurable effect
on the CMB anisotropies [Ma & Bertschinger, 1995,Dodelson et al, 1996].

For the ordinary matter or baryons,
&Omega_{b}~0.02*h*^{-2}
(*w*_{b}~0)
with statistical uncertainties at about the ten percent
level determined through studies of the light element
abundances (for reviews, see [Boesgaard & Steigman, 1985,Schramm & Turner, 1998,Tytler et al, 2000]). This value is
in strikingly good agreement with that implied by the CMB anisotropies themselves
as we shall see. There is very strong evidence that there is also substantial
non-baryonic dark matter. This dark matter must
be close to cold
(*w*_{m}=0)
for the gravitational instability paradigm to work [Peebles, 1982] and when added to the baryons gives
a total in non-relativistic matter of
&Omega_{m}~1/3.
Since the Universe appears to be flat, the total
&Omega_{tot}
must be equal to one. Thus, there is a missing component
to the inventory, dubbed *dark energy*, with
&Omega_{&Lambda} ~ 2/3.
The cosmological constant
(*w*_{&Lambda}=-1)
is only one of several possible candidates but we will
generally assume this form unless otherwise specified. Measurements of an accelerated
expansion from distant supernovae [Riess et al, 1998,Perlmutter et al, 1999] provide entirely
independent evidence for dark energy in this amount.

The initial spectrum of density perturbations
is assumed to be a power law with a power law index or tilt of *n*
~1
corresponding to a scale-invariant spectrum. Likewise the
initial spectrum of gravitational waves is assumed
to be scale-invariant, with an amplitude parameterized by the energy scale of
inflation *E*_{i}, and constrained to
be small compared with the initial density spectrum.
Finally the formation of structure will eventually reionize
the Universe at some redshift
7 < *z* < 20

Many of the features of the anisotropies will be produced even if these parameters fall outside the expected range or even if the standard paradigm is incorrect. Where appropriate, we will try to point these out.