21. The Cosmological Parameters
1
21. THE COSMOLOGICAL PARAMETERS
Updated September 2009, by O. Lahav (University College London) and A.R. Liddle
(University of Sussex).
21.1. Parametrizing the Universe
Rapid advances in observational cosmology have led to the establishment of a precision
cosmological model, with many of the key cosmological parameters determined to one
or two signiFcant Fgure accuracy. Particularly prominent are measurements of cosmic
microwave background (CMB) anisotropies, led by the Fve-year results from the Wilkinson
Microwave Anisotropy Probe (WMAP) [1–3]. However the most accurate model of the
Universe requires consideration of a wide range of di±erent types of observation, with
complementary probes providing consistency checks, lifting parameter degeneracies, and
enabling the strongest constraints to be placed.
The term ‘cosmological parameters’ is forever increasing in its scope, and nowadays
includes the parametrization of some functions, as well as simple numbers describing
properties of the Universe. The original usage referred to the parameters describing the
global dynamics of the Universe, such as its expansion rate and curvature. Also now of
great interest is how the matter budget of the Universe is built up from its constituents:
baryons, photons, neutrinos, dark matter, and dark energy. We need to describe the
nature of perturbations in the Universe, through global statistical descriptors such as
the matter and radiation power spectra. There may also be parameters describing the
physical state of the Universe, such as the ionization fraction as a function of time
during the era since recombination. Typical comparisons of cosmological models with
observational data now feature between Fve and ten parameters.
21.1.1.
The global description of the Universe
:
Ordinarily, the Universe is taken to be a perturbed Robertson–Walker space-time with
dynamics governed by Einstein’s equations. This is described in detail by Olive and
Peacock in this volume. Using the density parameters Ω
i
for the various matter species
and Ω
Λ
for the cosmological constant, the ²riedmann equation can be written
X
i
Ω
i
+Ω
Λ
−
1=
k
R
2
H
2
,
(21
.
1)
where the sum is over all the di±erent species of material in the Universe. This equation
applies at any epoch, but later in this article we will use the symbols Ω
i
and Ω
Λ
to refer
to the present values. A typical collection would be baryons, photons, neutrinos, and
dark matter (given charge neutrality, the electron density is guaranteed to be too small
to be worth considering separately and is included with the baryons).
The complete present state of the homogeneous Universe can be described by giving
the current values of all the density parameters and of the Hubble parameter
h
.Th
e
s
e
also allow us to track the history of the Universe back in time, at least until an epoch
where interactions allow interchanges between the densities of the di±erent species,
which is believed to have last happened at neutrino decoupling, shortly before Big
Bang Nucleosynthesis (BBN). To probe further back into the Universe’s history requires