Non-Linear Trans-Planckian Corrections of Spectra due to the Non-trivial Initial States

TL;DR

This paper investigates how non-linear trans-Planckian effects and non-trivial initial states, specifically excited-de Sitter modes, modify the primordial power spectrum during inflation, offering a finite, symmetry-preserving approach that extends previous linear correction models.

Contribution

It introduces a novel method using excited-de Sitter modes and a de Sitter background to compute non-linear trans-Planckian corrections to the inflationary power spectrum, preserving curved space-time symmetry.

Findings

Power spectrum corrections are non-linear and finite.

In the de Sitter limit, corrections reduce to linear forms.

The approach preserves space-time symmetry and extends previous models.

Abstract

Recent Planck results motivated us to use non-Bunch-Davies vacuum. In this paper, we use the excited-de Sitter mode as non-linear initial states during inflation to calculate the corrected spectra of the initial fluctuations of the scalar field. First, we consider the field in de Sitter space-time as background field and for the non-Bunch-Davies mode, we use the perturbation theory to the second order approximation. Also, unlike conventional renormalization method, we offer de Sitter space-time as the background instead Minkowski space-time. This approach preserve the symmetry of curved space-time and stimulate us to use excited mode. By taking into account this alternative mode and the effects of trans-Planckian physics, we calculate the power spectrum in standard approach and Danielsson argument. The calculated power spectrum with this method is finite, corrections of it is non-linear, and in de Sitter limit corrections reduce to linear form that obtained from several previous conventional methods.