Using the tilted flat-$\Lambda$CDM and the untilted non-flat $\Lambda$CDM inflation models to measure cosmological parameters from a compilation of observational data

Abstract

We use the physically-consistent tilted spatially-flat and untilted non-flat $\Lambda$CDM inflation models to constrain cosmological parameter values with the Planck 2015 cosmic microwave background (CMB) anisotropy data and recent Type Ia supernovae measurements, baryonic acoustic oscillations (BAO) data, growth rate observations, and Hubble parameter measurements. The most dramatic consequence of including the four non-CMB data sets is the significant strengthening of the evidence for non-flatness in the non-flat $\Lambda$CDM model, from 1.8$\sigma$ for the CMB data alone to 5.1$\sigma$ for the full data combination. The BAO data is the most powerful of the non-CMB data sets in more tightly constraining model parameter values and in favoring a spatially-closed Universe in which spatial curvature contributes about a percent to the current cosmological energy budget. The untilted non-flat $\Lambda$CDM model better fits the large-angle CMB temperature anisotropy angular spectrum and is more consistent with the Dark Energy Survey constraints on the current value of the rms amplitude of mass fluctuations ($\sigma_8$) as a function of the current value of the nonrelativistic matter density parameter ($\Omega_m$) but does not provide as good a fit to the smaller-angle CMB temperature anisotropy data as does the tilted flat-$\Lambda$CDM model. Some measured cosmological parameter values differ significantly between the two models, including the reionization optical depth and the baryonic matter density parameter, both of whose 2$\sigma$ ranges (in the two models) are disjoint or almost so.