Planck 2015 constraints on the non-flat $\Lambda$CDM inflation model

TL;DR

This study uses Planck 2015 CMB data to explore a non-flat, closed Lambda CDM model with quantum fluctuation-based power spectrum, finding it can fit data well and address some cosmological tensions.

Contribution

It introduces a consistent power spectrum for non-flat inflation models and demonstrates that a closed Lambda CDM model fits Planck data comparably to flat models.

Findings

Closed Lambda CDM model fits Planck data well

Model can partially explain low multipole CMB anomalies

Helps reconcile CMB and weak lensing A8_8 constraints

Abstract

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.