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.
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