We investigate the effects of nonzero spatial curvature on cosmic inflation in light of cosmic microwave background (CMB) anisotropy measurements from the Planck Legacy 2018 release and from the 2015 observing season of BICEP2 and the Keck Array. Even a small percentage of nonzero 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 toward 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 ${\mathrm{\Omega }}_{K,0}=-0.051\pm 0.017$ for a curvature extension of Lambda cold dark matter and ${\mathrm{\Omega }}_{K,0}=-0.031\pm 0.014$ for Starobinsky inflation. Model comparisons of various inflation models give similar results to flat universes with the Starobinsky model outperforming most other models.

• Received 18 May 2022
• Accepted 8 July 2022

DOI:https://doi.org/10.1103/PhysRevD.106.063529