Trans-Planckian Physics and the Spectrum of Fluctuations in a Bouncing Universe

TL;DR

This paper investigates how trans-Planckian physics influences the spectrum of scalar fluctuations in a bouncing universe, showing that modifications at short length scales can significantly alter the expected cosmological perturbation spectrum.

Contribution

It demonstrates that changes in dispersion relations at sub-Planckian scales can affect the fluctuation spectrum in bouncing cosmologies without ambiguity in initial conditions.

Findings

Spectrum depends on dispersion relation modifications

Amplitude and spectral index can vary

Spectrum can show modulations

Abstract

In this paper, we calculate the spectrum of scalar field fluctuations in a bouncing, asymptotically flat Universe, and investigate the dependence of the result on changes in the physics on length scales shorter than the Planck length which are introduced via modifications of the dispersion relation. In this model, there are no ambiguities concerning the choice of the initial vacuum state. We study an example in which the final spectrum of fluctuations depends sensitively on the modifications of the dispersion relation without needing to invoke complex frequencies. Changes in the amplitude and in the spectral index are possible, in addition to modulations of the spectrum. This strengthens the conclusions of previous work in which the spectrum of cosmological perturbations in expanding inflationary cosmologies was studied, and it was found that, for dispersion relations for which the evolution is not adiabatic, the spectrum changes from the standard prediction of scale-invariance.