Renormalization-group techniques for single-field inflation in primordial cosmology and quantum gravity

TL;DR

This paper applies renormalization-group techniques to single-field inflation, classifying spectral behaviors and identifying novel features and models consistent with or ruled out by observational data.

Contribution

It introduces an RG framework for inflation, classifies spectral types without specific model assumptions, and uncovers new spectral features and models beyond standard Lagrangian approaches.

Findings

Spectra with essential singularities in the coupling parameter.

Violations of the standard consistency relation $r+8n_{t}=0$.

RG classification helps identify observationally ruled-out models.

Abstract

We study inflation as a "cosmic" renormalization-group flow. The flow, which encodes the dependence on the background metric, is described by a running coupling $\alpha $, which parametrizes the slow roll, a de Sitter free, analytic beta function and perturbation spectra that are RG invariant in the superhorizon limit. Using RG invariance as a guiding principle, we classify the main types of flows according to the properties of their spectra, without referring to their origins from specific actions or models. Novel features include spectra with essential singularities in $\alpha $ and violations of the relation $r+8n_{\text{t}}=0$ to the leading order. Various classes of potentials studied in the literature can be described by means of the RG approach, even when the action includes a Weyl-squared term, while others are left out. In known cases, the classification helps identify the models that are ruled out by data. The RG approach is also able to generate spectra that cannot be derived from standard Lagrangian formulations.