Cosmic Microwave Background Observations: Implications for Hubble's Constant and the Spectral Parameters $\n$ and $Q$ in Cold Dark Matter Critical Density Universes

Abstract

Recent cosmic microwave background (CMB) measurements over a large range of angular scales have become sensitive enough to provide interesting constraints on cosmological parameters within a restricted class of models. We use the CMB measurements to study inflation-based, cold dark matter (CDM) critical density universes. We explore the 4-dimensional parameter space having as free parameters, Hubble's constant Ho, baryonic fraction Omega_b, the spectral slope of scalar perturbations n and the power spectrum quadrupole normalization Q. We calculate chi-squared minimization values and likelihood intervals for these parameters. Within the models considered, a low value for the Hubble constant is preferred: Ho= 30^{+18}_{-7} km/s/Mpc. The baryonic fraction is not as well-constrained by the CMB data: Omega_b = 0.07^{+ 0.24}_{-0.07}. The power spectrum slope is n=0.91^{+0.20}_{-0.12}. The power spectrum normalization is Q=18 +/- 2.5 uK. The error bars on each parameter are approximately 1 sigma and are for the case where the other 3 parameters have been marginalized. If we condition on n=1 we obtain the normalization Q = 17 +/- 1.0 uK. The permitted regions of the 4-D parameter space are presented in a series of 2-D projections. In the context of the CDM critical density universes considered here, current CMB data favor a low value for the Hubble constant. Such low-Ho models are consistent with Big Bang nucleosynthesis, cluster baryonic fractions, the large-scale distribution of galaxies and the ages of globular clusters; although in disagreement with direct determinations of the Hubble constant.