Scale-Dependent Loop Corrections to the Inflationary Power Spectrum

TL;DR

This paper develops a renormalisation framework for loop corrections to the inflationary power spectrum in non-de Sitter backgrounds, enabling consistent analysis of scale-dependent features and their implications for cosmological observations.

Contribution

It introduces a scale-dependent renormalisation procedure within the EFT of inflation applicable to backgrounds with broken de Sitter symmetry, including features.

Findings

Renormalisation cancels divergences with local counter-terms respecting EFT symmetries.

One-loop power spectrum with features vanishes at large and small scales.

Models with primordial features remain perturbative and consistent with observations.

Abstract

Loop corrections to primordial correlation functions are unavoidable due to the non-linear nature of gravity. Previous works have established a robust framework for computing the renormalised one-loop power spectra of scalar and tensor modes, but primarily in (near) de Sitter backgrounds. In this work, we develop a consistent renormalisation procedure applicable to inflationary backgrounds that strongly break de Sitter symmetries and generate scale-dependent features in the primordial spectra. Our analysis is performed within the Effective Field Theory (EFT) of inflationary fluctuations, allowing for arbitrary time dependence of the Wilson coefficients. We show that both ultraviolet divergences and tadpoles of the theory, despite their strong time and scale dependence, can be cancelled by a finite set of local counter-terms compatible with the EFT symmetries. Importantly, this result only relies on the existence of an initial phase of adiabatic evolution continuously related to the Bunch-Davies vacuum and holds independently of the precise time dependence of the background and of the free-field mode functions. We then study two concrete realisations, corresponding to resonant and sharp features. In both cases, all calculations are carried out exactly in the limit of small feature amplitude. We analyse perturbativity and provide the first explicit demonstration that the renormalised one-loop power spectrum generated by a localised feature along the inflationary trajectory vanishes both at large and small scales. Our scale-dependent renormalisation framework implies that models of primordial features used to fit CMB residuals are consistent with perturbativity bounds, and opens the door to systematic studies of loop corrections in more complicated scenarios relevant for scalar-induced gravitational waves and primordial black holes.