Second-Order Corrections to the Power Spectrum in the Slow-Roll Expansion with a Time-Dependent Sound Speed

TL;DR

This paper extends a Green's function method to compute the power spectrum of density perturbations with a time-dependent sound speed, providing second-order slow-roll corrections and including tachyon inflation as a special case.

Contribution

It introduces a second-order correction framework for the power spectrum with a time-dependent sound speed in slow-roll inflation models.

Findings

Derived explicit power spectrum and spectral index up to second-order corrections.

Included tachyon inflation as a special case in the analysis.

Enhanced accuracy of density perturbation predictions in inflation models.

Abstract

We extend Green's function method developed by Stewart and Gong to calculate the power spectrum of density perturbation in the case with a time-dependent sound speed, and explicitly give the power spectrum and spectral index up to second-order corrections in the slow-roll expansion. The case of tachyon inflation is included as a special case.