Exact Mapping between Tensor and Most General Scalar Power Spectra

TL;DR

This paper establishes an exact relation between tensor and scalar primordial power spectra in inflation, simplifying calculations by deriving scalar spectra from tensor modes, demonstrated through higher-order spectrum derivation.

Contribution

It introduces an exact mapping between tensor and scalar power spectra, streamlining the derivation process in inflationary models.

Findings

Derived the next-to-next-to-leading order scalar power spectrum from tensor modes.

Simplified the computation of scalar spectra using tensor mode analysis.

Validated the mapping with generalized single field inflation models.

Abstract

We prove an exact relation between the tensor and the scalar primordial power spectra generated during inflation. Such a mapping considerably simplifies the derivation of any power spectra as they can be obtained from the study of the tensor modes only, which are much easier to solve. As an illustration, starting from the second order slow-roll tensor power spectrum, we derive in a few lines the next-to-next-to-leading order power spectrum of the comoving curvature perturbation in generalized single field inflation with a varying speed of sound.