Perturbation Spectra and Renormalization-Group Techniques in Double-Field Inflation and Quantum Gravity Cosmology

TL;DR

This paper investigates two-field inflation in quantum gravity, revealing how RG invariance guides the identification of perturbations and confirms predictions of single-field inflation at leading order.

Contribution

It introduces a perturbative regime in double-field inflation coupled with quantum gravity, utilizing RG invariance to identify physical perturbations and compute power spectra.

Findings

RG invariance helps identify correct perturbations on superhorizon scales

Predictions of single-field inflation are confirmed at leading order

Power spectra computed to NNLL and NLL orders

Abstract

We study primordial cosmology with two scalar fields that participate in inflation at the same time, by coupling quantum gravity (i.e., the theory $R+R^{2}+C^{2}$ with the fakeon prescription/projection for $C^{2}$) to a scalar field with a quadratic potential. We show that there exists a perturbative regime that can be described by an asymptotically de Sitter, cosmic RG flow in two couplings. Since the two scalar degrees of freedom mix in nontrivial ways, the adiabatic and isocurvature perturbations are not RG invariant on superhorizon scales. It is possible to identify the correct perturbations by using RG invariance as a guiding principle. We work out the resulting power spectra of the tensor and scalar perturbations to the NNLL and NLL orders, respectively. An unexpected consequence of RG invariance is that the theory remains predictive. Indeed, the scalar mixing affects only the subleading corrections, so the predictions of quantum gravity with single-field inflation are confirmed to the leading order.