Adiabatic regularisation of power spectra in $k$-inflation

TL;DR

This paper investigates the impact of adiabatic UV regularisation on the power spectrum in slow-roll and non-minimal $k$-inflation models, finding negligible effects under typical conditions and establishing frame equivalence.

Contribution

It demonstrates that adiabatic regularisation does not alter the power spectrum in slow-roll $k$-inflation up to second order, and proves the equivalence of regularisation in Jordan and Einstein frames.

Findings

No difference in power spectrum after regularisation in typical slow-roll $k$-inflation.

Regularisation subtraction terms are equivalent in Jordan and Einstein frames.

Extends analysis to non-minimal $k$-inflation models.

Abstract

We look at the question posed by Parker et al. about the effect of UV regularisation on the power spectrum for inflation. Focusing on the slow-roll $k$-inflation, we show that up to second order in the Hubble and sound flow parameters, the adiabatic regularisation of such model leads to no difference in the power spectrum apart from certain cases that violate near scale invariant power spectra. Furthermore, extending to non-minimal $k$-inflation, we establish the equivalence of the subtraction terms in the adiabatic regularisation of the power spectrum in Jordan and Einstein frames.