Cosmological $\alpha'$-corrections from the functional renormalization group

TL;DR

This paper uses the Functional Renormalization Group in string theory to derive an all-orders effective action for cosmological backgrounds, revealing a non-Gaussian UV fixed point and discussing implications for cosmology.

Contribution

It introduces a novel application of the Functional Renormalization Group to string cosmology, deriving all-orders corrections and analyzing fixed points in various dimensions.

Findings

Exact non-analytic solution in any dimension D

Non-Gaussian UV fixed point with positive Newton coupling in D near 2

No evidence of similar fixed point in D=4 within polynomial truncations

Abstract

We employ the techniques of the Functional Renormalization Group in string theory, in order to derive an effective mini-superspace action for cosmological backgrounds to all orders in the string scale $\alpha'$. To this end, T-duality plays a crucial role, classifying all perturbative curvature corrections in terms of a single function of the Hubble parameter. The resulting renormalization group equations admit an exact, albeit non-analytic, solution in any spacetime dimension $D$, which is however incompatible with Einstein gravity at low energies. Within an $\epsilon$-expansion about $D=2$, we also find an analytic solution which exhibits a non-Gaussian ultraviolet fixed point with positive Newton coupling, as well as an acceptable low-energy limit. Yet, within polynomial truncations of the full theory space, we find no evidence for an analog of this solution in $D=4$. Finally, we comment on potential cosmological implications of our findings.