Effects of Quantum Deformations on the Spectrum of Cosmological Perturbations

TL;DR

This paper investigates how quantum deformations of the wave equation influence the power spectrum of cosmological perturbations during inflation, revealing deviations from standard results and potential observational signatures.

Contribution

It introduces a quantum deformation framework for the wave equation in cosmology and analyzes its effects on the inflationary power spectrum.

Findings

Deformation causes noticeable deviations in the scalar and tensor spectra.

In de Sitter inflation, the spectrum remains scale invariant despite deformation.

The spectrum's deviation depends on the deformation parameter, with a generic modulation feature.

Abstract

We consider a quantum deformation of the wave equation on a cosmological background as a toy-model for possible trans-Planckian effects. We compute the power spectrum of scalar and tensor fluctuations for power-law inflation, and find a noticeable deviation from the standard result. We consider de Sitter inflation as a special case, and find that the resulting power spectrum is scale invariant. For both inflationary scenarios the departure from the standard spectrum is sensitive to the size of the deformation parameter. A modulation in the power spectrum appears to be a generic feature of the model.