Inflationary Hubble Parameter from the Gravitational Wave Spectrum in the General Slow-roll Approximation

TL;DR

This paper derives improved general slow-roll formulas for the primordial gravitational wave spectrum, including inverse formulas to determine the Hubble parameter from the spectrum, and establishes a consistency condition linking scalar and tensor spectra.

Contribution

It introduces new inverse formulas for the Hubble parameter based on the gravitational wave spectrum within the general slow-roll framework.

Findings

Derived first and second order inverse formulas for H

Established a general slow-roll consistency condition

Enhanced the accuracy of primordial gravitational wave spectrum calculations

Abstract

Improved general slow-roll formulae giving the primordial gravitational wave spectrum are derived in the present work. Also the first and second order general slow-roll inverse formulae giving the Hubble parameter $H$ in terms of the gravitational wave spectrum are derived. Moreover, the general slow-roll consistency condition relating the scalar and tensor spectra is obtained.