Cosmological models and constraints 241spectra are generally defined so thatnT=0 corresponds to scale invariant,
in contrast to the scalar case.- Optionally, more parameters describing either departures of the scalar
perturbations from a power law (e.g. Kosowsky and Turner 1995) or a small
admixture of isocurvature perturbations.
Other miscellaneous parameters include:
- A significant neutrino massmν. None of the current neutrino oscillation
results favour a cosmologically interesting neutrino mass. - The effective number of neutrino speciesNν. This quantity includes any
particle species which is relativistic when it decouples or can model entropy
production prior to last scattering. - The redshift of reionization,zr. Spectra of quasars at redshiftz=5show
that the universe has been reionized at least since then.
A realistic parameter analysis might include at least eight free parameters.
Given a particular microwave background measurement, deciding on a particular
set of parameters and various priors on those parameters is as much art as science.
For the correct model, parameter values should be insensitive to the size of the
parameter space or the particular priors invoked. Several particular parameter
space analyses are mentioned in section 7.5.5.
7.5.2 Physical quantities
While these parameters are useful and conventional for characterizing
cosmological models, the features in the microwave background power spectrum
depend on various physical quantities which can be expressed in terms of the
parameters. Here the physical quantities are summarized, and their dependence
on parameters given. This kind of analysis is important for understanding the
model space of parameters as more than just a black box producing output power
spectra. All of the physical dependences discussed here can be extracted from
Hu and Sugiyama (1996). By comparing numerical solutions with the evolution
equations, Hu and Sugiyama demonstrated that they had accounted for all relevant
physical processes.
Power-law initial conditions are determined in a straightforward way by the
appropriate parametersQ,n,randnT, if the perturbations are purely adiabatic.
Additional parameters must be used to specify any departure from power-law
spectra or to specify an additional admixture of isocurvature initial conditions
(e.g. Bucheret al1999). These parameters directly express physical quantities.
However, the physical parameters determining the evolution of the
initial perturbations until decoupling involve a few specific combinations of
cosmological parameters. First, note that the density of radiation is fixed by
the current microwave background temperature which is known from COBE,
as well as the density of the neutrino backgrounds. The gravitational potentials