Signatures of trans-Planckian dispersion in inflationary spectra

TL;DR

This paper investigates how trans-Planckian dispersion relations affect inflationary spectra, showing that modifications depend on the deviation parameter and are robust, impacting potential reconstruction.

Contribution

It provides a generic analysis of leading-order modifications to inflationary spectra due to trans-Planckian dispersion relations, including the case where H and Lambda are comparable.

Findings

Modifications scale as (H/Lambda)^alpha for all alpha, except for discrete higher powers.

Modifications are robust against higher-order dispersion terms.

Reconstruction of the inflaton potential requires assumptions about the dispersion relation.

Abstract

The primordial spectra are calculated using dispersion relations which deviate from the relativistic one above a certain energy scale Lambda. We determine the properties of the leading modifications with respect to the standard spectra when Lambda is much greater than H, the Hubble scale during inflation. To be generic, we parameterize the lowest order deviation from the relativistic law by alpha, the power of P/Lambda where P is the proper momentum. When working in the asymptotic vacuum, the leading modification scales as (H/Lambda)^alpha for all alpha, except for a discrete set where the power is higher. Moreover, this modification is robust against introducing higher order terms in the dispersion relation. We then algebraically deduce the modifications of scalar and tensor power spectra in slow roll inflation from modifications calculated in de Sitter space. The modifications do not exhibit oscillations unless the dispersion relation induces some non-adiabaticity near a given scale. Finally, we explore the much less studied regime where H and Lambda are comparable. Our results indicate that the project of reconstructing the inflaton potential cannot be pursued without making some hypothesis about the dispersion relation of the fluctuation modes.