Constraints on the Sharpness of the Curvature Power Spectrum

TL;DR

This paper investigates the theoretical limits on how sharply peaked the curvature power spectrum can be during inflation, emphasizing energy conservation constraints and analyzing specific inflaton models.

Contribution

It provides a general theoretical framework constraining the sharpness of the curvature spectrum, independent of inflaton potential details, and examines concrete models.

Findings

Energy conservation significantly constrains spectrum sharpness.

Constraints are independent of inflaton potential form.

Concrete models show limits are saturated in certain cases.

Abstract

Motivated by the fact that a sharply peaked curvature spectrum is often considered in the literature, we examine theoretical constraints on the sharpness of such a spectrum. In particular, we show that the sharply peaked curvature power spectrum, originating from the enhancement of subhorizon perturbations during inflation, is significantly constrained by energy conservation. While the constraints do not depend on the exact form of inflaton potential, we also study concrete inflaton potentials that realize a sharply peaked curvature spectrum and how theoretical limits are saturated in these cases.