Perturbation spectra and renormalization-group techniques in double-field inflation and quantum gravity cosmology

Abstract

We study primordial cosmology with two scalar fields that participate ininflation at the same time, by coupling quantum gravity (i.e., the theory R+R2+C2 with the fakeon prescription/projection for C2) to ascalar field with a quadratic potential. We show that there exists aperturbative regime that can be described by an asymptotically de Sitter,cosmic RG flow in two couplings. Since the two scalar degrees of freedom mixin nontrivial ways, the adiabatic and isocurvature perturbations are not RGinvariant on superhorizon scales. It is possible to identify the correctperturbations by using RG invariance as a guiding principle. We work out theresulting power spectra of the tensor and scalar perturbations to the NNLLand NLL orders, respectively. An unexpected consequence of RG invariance isthat the theory remains predictive. Indeed, the scalar mixing affects onlythe subleading corrections, so the predictions of quantum gravity withsingle-field inflation are confirmed to the leading order.