The Corley-Jacobson dispersion relation and trans-Planckian inflation

TL;DR

This paper investigates how trans-Planckian physics might influence inflationary fluctuation spectra, comparing different analytical methods and providing new exact results to better understand these effects.

Contribution

It introduces a new exact analytical solution for the Corley-Jacobson dispersion relation in inflationary cosmology and analyzes the impact of method choices on the spectrum.

Findings

Derived a new exact analytical expression for the dispersion relation.

Compared the WKB approximation with exact results, highlighting differences.

Showed the dependence of the fluctuation spectrum on matching time choices.

Abstract

In this Letter we study the dependence of the spectrum of fluctuations in inflationary cosmology on possible effects of trans-Planckian physics, using the Corley/Jacobson dispersion relations as an example. We compare the methods used in previous work [1] with the WKB approximation, give a new exact analytical result, and study the dependence of the spectrum obtained using the approximate method of Ref. [1] on the choice of the matching time between different time intervals. We also comment on recent work subsequent to Ref. [1] on the trans-Planckian problem for inflationary cosmology.