Analytic formula for the dynamics around inflation end and implications on primordial gravitational waves

TL;DR

This paper derives an analytic formula describing the evolution of the Hubble parameter at the end of inflation, enabling the prediction of a spectral break in primordial gravitational waves that reveals inflationary energy scales.

Contribution

It provides a novel analytic approach to model the Hubble parameter's behavior at inflation's end and predicts the resulting gravitational wave spectrum's features.

Findings

Analytic formula for Hubble parameter evolution at inflation end

Prediction of spectral break in primordial gravitational waves

Potential to determine inflation energy scale and reheating temperature

Abstract

We argue that primordial gravitational waves have a spectral break and its information is quite useful for exploring the early universe. Indeed, such a spectral break can be a fingerprint of the end of inflation, and the amplitude and the frequency at the break can tell us the energy scale of inflation and the reheating temperature simultaneously. In order to investigate the spectral break, we give an analytic formula for evolution of the Hubble parameter around the end of inflation where the slow roll approximation breaks down. We also evaluate the spectrum of primordial gravitational waves around the break point semi-analytically using the analytic formula for the inflation dynamics.