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We constrain tilted spatially-flat and untilted nonflat XCDM dynamical darkenergy inflation parameterizations using Planck 2015 cosmic microwavebackground (CMB) anisotropy data and recent baryonic acoustic oscillationsdistance measurements, Type Ia supernovae data, Hubble parameter observations,and growth rate measurements. Inclusion of the four non-CMB data sets resultsin a significant strengthening of the evidence for nonflatness in the nonflatXCDM model from 1.1$\sigma$ for the CMB data alone to 3.4$\sigma$ for the fulldata combination. In this untilted nonflat XCDM case the data favor aspatially-closed model in which spatial curvature contributes a little lessthan a percent of the current cosmological energy budget; they also mildlyfavor dynamical dark energy over a cosmological constant at 1.2$\sigma$. Thesedata 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 isunable to rule out dark energy dynamics. The nonflat XCDM parameterization iscompatible with the Dark Energy Survey limits on the present value of the rmsmass fluctuations amplitude ($\sigma_8$) as a function of the present value ofthe nonrelativistic matter density parameter ($\Omega_m$), however it does notprovide as good a fit to the higher multipole CMB temperature anisotropy dataas does the standard tilted flat-$\Lambda$CDM model. A number of measuredcosmological parameter values differ significantly when determined using thetilted flat-XCDM and the nonflat XCDM parameterizations, including the baryonicmatter density parameter and the reionization optical depth.

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