Higher Order Corrections to Asymptotic-de Sitter Inflation

TL;DR

This paper examines how trans-Planckian physics influences the primordial power spectrum during inflation, revealing higher order corrections sensitive to the geometry and initial vacuum choice, applicable to various asymptotic de Sitter spaces.

Contribution

It introduces a method to calculate trans-Planckian corrections to the inflationary power spectrum using asymptotic de Sitter modes, highlighting geometry-dependent effects.

Findings

Power spectrum corrections depend on the choice of space-time parameter c.

Results are valid for any asymptotic de Sitter space-time.

Corrections include higher order and harmonic terms sensitive to space-time fluctuations.

Abstract

Since trans-Planckian considerations can be associated with the re-definition of the initial vacuum, we investigate further the influence of trans-Planckian physics on the spectra produced by the initial quasi-de Sitter (dS) state during inflation. We use the asymptotic-dS mode to study the trans-Planckian correction of the power spectrum to the quasi-dS inflation. The obtained spectra consist of higher order corrections associated with the type of geometry and harmonic terms sensitive to the fluctuations of space-time (or gravitational waves) during inflation. As an important result, the amplitude of the power spectrum is dependent on the choice of $c$, i.e. the type of space-time in the period of inflation. Also, the results are always valid for any asymptotic dS space-time and particularly coincide with the conventional results for dS and flat space-time.