Higher Order Corrections to the Primordial Gravitational Wave Spectrum and its Impact on Parameter Estimates for Inflation

TL;DR

This paper examines how higher order corrections to the primordial gravitational wave spectrum affect parameter estimation in inflation models, highlighting potential inaccuracies from spectrum approximation methods in future gravitational wave experiments.

Contribution

It derives higher order terms of the spectrum expansion up to sixth order and assesses their impact on inflationary parameter estimation accuracy.

Findings

Higher order corrections improve spectrum prediction accuracy.

Truncating the series can lead to incorrect parameter estimates.

Including more terms reduces deviation from numerical results.

Abstract

We study the impact of the use of the power series expression for the primordial tensor spectrum on parameter estimation from future direct detection gravitational wave experiments. The spectrum approximated by the power series expansion may give large deviation from the true (fiducial) value when it is normalized at CMB scale because of the large separation between CMB and direct detection scales. We derive the coefficients of the higher order terms of the expansion up to the sixth order within the framework of the slow-roll approximation and investigate how well the inclusion of higher order terms improves the analytic prediction of the spectrum amplitude by comparing with numerical results. Using the power series expression, we consider future constraints on inflationary parameters expected from direct detection experiments of the inflationary gravitational wave background and show that the truncation of the higher order terms can lead to incorrect evaluation of the parameters. We present two example models; a quadratic chaotic inflation model and mixed inflaton and curvaton model with a quartic inflaton potential.