Inflation in the closed FLRW model and the CMB

TL;DR

This paper investigates how spatial curvature in a closed FLRW universe affects inflationary dynamics and CMB anisotropies, showing curvature-induced modifications at large scales that could explain low multipole anomalies.

Contribution

It provides a detailed analysis of inflation in a closed universe, deriving the primordial power spectrum and comparing it with Planck data to assess curvature effects on CMB anomalies.

Findings

Curvature modifies inflationary dynamics and the primordial power spectrum.

Low multipole power deficit can be explained by positive spatial curvature.

Planck parameter estimates remain robust despite curvature effects.

Abstract

Recent cosmic microwave background (CMB) observations put strong constraints on the spatial curvature via estimation of the parameter $\Omega_k$ assuming an almost scale invariant primordial power spectrum. We study the evolution of the background geometry and gauge-invariant scalar perturbations in an inflationary closed FLRW model and calculate the primordial power spectrum. We find that the inflationary dynamics is modified due to the presence of spatial curvature, leading to corrections to the nearly scale invariant power spectrum at the end of inflation. When evolved to the surface of last scattering, the resulting temperature anisotropy spectrum ($C_{\ell}^{TT}$) shows deficit of power at low multipoles ($\ell<20$). By comparing our results with the recent Planck data we discuss the role of spatial curvature in accounting for CMB anomalies and in the estimation of the parameter $\Omega_k$. Since the curvature effects are limited to low multipoles, the Planck estimation of cosmological parameters remains robust under inclusion of positive spatial curvature.