  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 $\Lambda$CDM
model. Unlike earlier analyses of non-flat models, which assumed an
inconsistent power-law power spectrum of energy density inhomogeneities, we
find that the Planck 2015 data alone, and also in conjunction with baryon
acoustic oscillation measurements, are reasonably well fit by a closed
$\Lambda$CDM model in which spatial curvature contributes a few 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 $\Lambda$CDM model has reduced power, relative to the tilted,
spatially-flat $\Lambda$CDM case, and can 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. Our
results are interesting but tentative; a more thorough analysis is needed to
properly gauge their significance.
