Revisiting the Ultraviolet Tail of the Primordial Gravitational Wave

TL;DR

This paper investigates the ultraviolet tail of primordial gravitational waves, revealing its origin from the inflation-to-post-inflation transition and providing a semi-analytical spectrum with implications for detection.

Contribution

It introduces a semi-analytical expression for the UV tail of PGWs and clarifies the origin of divergences, considering finite transition durations and post-inflationary stages.

Findings

UV tail decays exponentially with a rate depending on transition speed

Stiff post-inflationary stage leads to a power-law and exponential spectral shape

Proposes a fitting formula for signal searches

Abstract

High-frequency primordial gravitational waves (PGWs) with wave numbers larger than the Hubble parameter at the end of inflation are originated from the ultraviolet (UV) modes, which are never stretched out of the horizon. Such a UV tail of the PGW energy spectrum has a spurious logarithmic divergence. We study the origin of such a divergence, and find that it comes from the instantaneous inflation-to-post-inflation transition, which can be removed by considering a finite duration. For the first time, we obtain a semi-analytical expression for the PGW energy spectrum. We find that the UV tail decays exponentially, while the decay rate depends solely on the transition rate. When there is a stiff post-inflationary stage, the enhanced PGW displays a characteristic spectral shape of power-law increasing and exponential decaying. We propose a fitting formula which can be used for signal searching.