Trans-Planckian Physics from a Nonlinear Dispersion Relation

TL;DR

This paper investigates how nonlinear dispersion relations affect the power spectrum of scalar fields during inflation, highlighting the limitations of the WKB approximation and providing numerical and semi-analytical results for trans-Planckian corrections.

Contribution

It introduces a specific nonlinear dispersion relation model and analyzes its impact on the inflationary power spectrum using numerical and semi-analytical methods, challenging previous assumptions about the WKB approximation.

Findings

WKB approximation is valid only for $k \gg aH$

Corrections to the power spectrum depend on the dispersion relation details

Numerical methods reveal significant deviations from standard predictions

Abstract

We study a particular nonlinear dispersion relation $\omega_p(k_p)$ -- a series expansion in the physical wavenumber $k_p$ -- for modeling first-order corrections in the equation of motion of a test scalar field in a de Sitter spacetime from trans-Planckian physics in cosmology. Using both a numerical approach and a semianalytical one, we show that the WKB approximation previously adopted in the literature should be used with caution, since it holds only when the comoving wavenumber $k\gg aH$. We determine the amplitude and behavior of the corrections on the power spectrum for this test field. Furthermore, we consider also a more realistic model of inflation, the power-law model, using only a numerical approach to determine the corrections on the power spectrum.