is related to the usual index, ns, by vs= ns−1.] The transport problem (see below) is dependent upon physical processes, and hence on physical parameters. A partial list includes the Hubble parameter h, various mean energy densities [Ωtot, ΩB, ΩΛ, Ωcdm, Ωhdm]h2, and parameters characterizing the ionization history of the Universe—e.g., the Compton optical depth τC from a reheating redshift zreh to the present. Instead of Ωtot, we prefer to use the curvature energy parameter, Ωk≡1−Ωtot, thus zero for the flat case. In this space, the Hubble parameter h=(Σj(Ωjh2))1/2, and the age of the Universe, t0, are functions of the Ωjh2. The density in nonrelativistic (clustering) particles is Ωnr=ΩB+Ωcdm+Ωhdm. The density in relativistic particles, Ωer, includes photons, relativistic neutrinos, and decaying particle products, if any, Ωer, the abundance of primordial helium, etc., should also be considered as parameters to be determined. The count is thus at least 17. Estimates of errors on a smaller 9-parameter inflation set for the MAP and Planck satellites are given in the final section.
The arena in which CMB theory battles observation is the anisotropy power spectrum in multipole space. Fig. 2, which shows how primary Cℓ values vary with some of these cosmic parameters. Here The
For a given model, the early universe is uniquely related to late-time power spectrum measures of relevance for the CMB, such as the quadrupole or averages over ℓ-bands B, and to LSS measures, such as the rms density fluctuation level on the 8 h−1 Mpc (cluster) scale, σ8, so any of these can be used in