Relics of spatial curvature in the primordial non-gaussianity

TL;DR

This paper investigates how residual spatial curvature from the early universe could leave subtle signatures in the CMB, particularly in non-gaussianity, but these effects are challenging to detect with current technology.

Contribution

It provides a detailed analysis of how primordial spatial curvature affects CMB power spectrum and non-gaussianity, highlighting the potential observational signatures.

Findings

Power spectrum corrections are minimal and hard to detect.

Non-gaussianity parameter f_NL can be affected on large scales.

Maximum predicted f_NL is around 0.3, below current detection thresholds.

Abstract

We study signatures in the Cosmic Microwave Background (CMB) induced by the presence of strong spatial curvature prior to the epoch of inflation which generated our present universe. If inflation does not last sufficiently long to drive the large-scale spatial curvature to zero, then presently observable scales may have left the horizon while spatial slices could not be approximated by a flat, Euclidean geometry. We compute corrections to the power spectrum and non-gaussianity of the CMB temperature anisotropy in this scenario. The power spectrum does not receive significant corrections and is a weak diagnostic of the presence of curvature in the initial conditions, unless its running can be determined with high accuracy. However, the bispectral non-gaussianity parameter f_NL receives modifications on the largest observable scales. We estimate that the maximum signal would correspond to f_NL ~ 0.3, which is out of reach for present-day microwave background experiments.