  We study Planck 2015 cosmic microwave background (CMB) anisotropy data using
the energy density inhomogeneity power spectrum generated by quantum
fluctuations during an early epoch of inflation in the non-flat XCDM model.
Here dark energy is parameterized using a fluid with a negative equation of
state parameter but with the speed of fluid acoustic inhomogeneities set to the
speed of light. We use this simple parameterization of dynamical dark energy,
that is relatively straightforward to use in a computation, in a first attempt
to gain some insight into how dark energy dynamics and non-zero spatial
curvature jointly affect the CMB anisotropy data constraints. Unlike earlier
analyses of non-flat models, we use a physically consistent power spectrum for
energy density inhomogeneities. We find that the Planck 2015 data in
conjunction with baryon acoustic oscillation measurements are reasonably well
fit by a closed XCDM model in which spatial curvature contributes a percent of
the current cosmological energy density budget. In this model, the measured
Hubble constant and non-relativistic matter density parameter are in good
agreement with values determined using most other data. Depending on parameter
values, the closed XCDM model has reduced power, relative to the tilted,
spatially-flat $\Lambda$CDM case, and appears to partially alleviate the low
multipole CMB temperature anisotropy deficit and can help partially reconcile
the CMB anisotropy and weak lensing $\sigma_8$ constraints, at the expense of
somewhat worsening the fit to higher multipole CMB temperature anisotropy data.
However, the closed XCDM inflation model does not seem to improve the agreement
much, if at all, compared to the closed $\Lambda$CDM inflation case, even
though it has one more free parameter. Our results are interesting but
tentative; a more thorough analysis is needed to properly gauge their
significance.
