Cosmic inflation as a renormalization-group flow: the running of power spectra in quantum gravity

TL;DR

This paper models the evolution of inflationary power spectra as a renormalization-group flow in quantum gravity, deriving spectral indices and their runnings with next-to-leading order precision, and predicting testable quantum gravity effects.

Contribution

It introduces a novel RG flow framework for inflationary spectra in quantum gravity with fakeons, including next-to-leading order calculations and new quantum gravity predictions.

Findings

Spectral indices and their runnings are computed to next-to-leading log order.

Universal relations between spectra are established.

Corrections to the $r=-8n_{T}$ relation are derived.

Abstract

We study the running of power spectra in inflationary cosmology as a renormalization-group flow from the de Sitter fixed point. The beta function is provided by the equations of the background metric. The spectra of the scalar and tensor fluctuations obey RG evolution equations with vanishing anomalous dimensions in the superhorizon limit. By organizing the perturbative expansion in terms of leading and subleading logs, we calculate the spectral indices, their runnings, the runnings of the runnings, etc., to the next-to-leading log order in quantum gravity with fakeons (i.e., the theory $R+R^{2}+C^{2}$ with the fakeon prescription/projection for $C^{2}$). We show that these quantities are related to the spectra in a universal way. We also compute the first correction to the relation $r=-8n_{T}$ and provide a number of quantum gravity predictions that can be hopefully tested in the forthcoming future.