Observational constraints on the tilted flat-XCDM and the untilted nonflat XCDM dynamical dark energy inflation parameterizations

We constrain tilted spatially-flat and untilted nonflat XCDM dynamical dark energy inflation parameterizations using Planck 2015 cosmic microwave background (CMB) anisotropy data and recent baryonic acoustic oscillations distance measurements, Type Ia supernovae data, Hubble parameter observations, and growth rate measurements. Inclusion of the four non-CMB data sets results in a significant strengthening of the evidence for nonflatness in the nonflat XCDM model from 1.1$\sigma$ for the CMB data alone to 3.4$\sigma$ for the full data combination. In this untilted nonflat XCDM case the data favor a spatially-closed model in which spatial curvature contributes a little less than a percent of the current cosmological energy budget; they also mildly favor dynamical dark energy over a cosmological constant at 1.2$\sigma$. These data are also better fit by the flat-XCDM parameterization than by the standard $\Lambda$CDM model, but only at 0.3$\sigma$ significance. Current data is unable to rule out dark energy dynamics. The nonflat XCDM parameterization is compatible with the Dark Energy Survey limits on the present value of the rms mass fluctuations amplitude ($\sigma_8$) as a function of the present value of the nonrelativistic matter density parameter ($\Omega_m$), however it does not provide as good a fit to the higher multipole CMB temperature anisotropy data as does the standard tilted flat-$\Lambda$CDM model. A number of measured cosmological parameter values differ significantly when determined using the tilted flat-XCDM and the nonflat XCDM parameterizations, including the baryonic matter density parameter and the reionization optical depth.