Finite inflation in curved space

TL;DR

This paper examines how small spatial curvature affects cosmic inflation and CMB observations, finding a preference for closed universes and implications for inflation duration and primordial power spectrum features.

Contribution

It provides Bayesian analysis showing the preference for closed universes and explores the impact of curvature on inflation models and CMB data interpretation.

Findings

CMB data favor closed universes with high Bayesian odds.

Curvature influences the primordial power spectrum, causing oscillations and large-scale cutoff.

Starobinsky inflation remains the most favored model among those tested.

Abstract

We investigate the effects of non-zero spatial curvature on cosmic inflation in the light of cosmic microwave background (CMB) anisotropy measurements from the Planck 2018 legacy release and from the 2015 observing season of BICEP2 and the Keck Array. Even a small percentage of non-zero curvature today would significantly limit the total number of e-folds of the scale factor during inflation, rendering just-enough inflation scenarios with a kinetically dominated or fast-roll stage prior to slow-roll inflation more likely. Finite inflation leads to oscillations and a cutoff towards large scales in the primordial power spectrum and curvature pushes them into the CMB observable window. Using nested sampling, we carry out Bayesian parameter estimations and model comparisons taking into account constraints from reheating and horizon considerations. We confirm the preference of CMB data for closed universes with Bayesian odds of over $100:1$ and with a posterior on the curvature density parameter of $\Omega_{K,0}=-0.051\pm0.017$ for a curvature extension of LCDM and $\Omega_{K,0}=-0.031\pm0.014$ for Starobinsky inflation. Model comparisons of various inflation models give similar results as for flat universes with the Starobinsky model outperforming most other models.