ar X iv : a st ro - p h / 98 09 04 3 v 1 4 S ep 1 99 8 Constraining Large Scale Structure Theories with the Cosmic Background Radiation

The case is strong that cosmic microwave background (CMB) and large scale structure (LSS) observations can be combined to determine the theory of structure formation and the cosmological parameters that define it. We review: the relevant 10+ parameters associated with the inflation model of fluctuation generation and the matter content of the Universe; the relation between LSS and primary and secondary CMB anisotropy probes as a function of wavenumber; how COBE constraints on energy injection rule out explosions as a dominant source of LSS; and how current anisotropy band-powers in multipole-space, at levels ∼ (10−5)2, strongly support the gravitational instability theory and suggest the universe could not have reionized too early. We use Bayesian analysis methods to determine what current CMB and CMB+LSS data imply for inflation-based Gaussian fluctuations in tilted ΛCDM, ΛhCDM and oCDM model sequences with cosmological age 11-15 Gyr, consisting of mixtures of baryons, cold “c” (and possibly hot “h”) dark matter, vacuum energy “Λ”, and curvature energy “o” in open cosmologies. For example, we find the slope of the initial spectrum is within about 5% of the (preferred) scale invariant form when just the CMB data is used, and for ΛCDM when LSS data is combined with CMB; with both, a nonzero value of ΩΛ is strongly preferred (≈ 2/3 for a 13 Gyr sequence, similar to the value from SNIa). The oCDM sequence prefers Ωtot < 1, but is overall much less likely than the flat ΩΛ 6= 0 sequence with CMB+LSS. We also review the rosy forecasts of angular power spectra and parameter estimates from future balloon and satellite experiments when foreground and systematic effects are ignored to show where cosmic parameter determination can go with just CMB information alone.