Large Field Inflation and Gravitational Entropy

TL;DR

This paper demonstrates that large field inflation models remain consistent with the covariant entropy bound when properly renormalized, even with many light species, by relating the physical Planck scale to the number of species and analyzing gravitational entropy.

Contribution

It shows that the apparent problems with many light species in large field inflation are resolved through correct renormalization, preserving the covariant entropy bound.

Findings

Gravitational entropy obeys the covariant entropy bound after proper renormalization.

The number of light species cancels out in the gravitational entropy calculation at leading order.

The axion decay constant is not necessarily the cutoff scale of semiclassical gravity.

Abstract

Large field inflation can be sensitive to perturbative and nonperturbative quantum corrections that spoil slow roll. A large number $N$ of light species in the theory, which occur in many string constructions, can amplify these problems. One might even worry that in a de Sitter background, light species will lead to a violation of the covariant entropy bound at large $N$. If so, requiring the validity of the covariant entropy bound could limit the number of light species and their couplings, which in turn could severely constrain axion-driven inflation. Here we show that there is no such problem when we correctly renormalize models with many light species, taking the {\it physical} Planck scale to be $M^2_{pl} \gtrsim N {\cal M}_{UV}^2$, where ${\cal M}_{UV}$ is the cutoff for the QFT coupled to semiclassical quantum gravity. The number of light species then cancels out of the gravitational entropy of de Sitter or near-de Sitter backgrounds at leading order. Working in detail with $N$ scalar fields in de Sitter space, renormalized to one loop order, we show that the gravitational entropy automatically obeys the covariant entropy bound. Furthermore, while the axion decay constant is a strong coupling scale for the axion dynamics, we show that it is {\it not} in general the cutoff of 4d semiclassical gravity. After renormalizing the two point function of the inflaton, we note that it is also controlled by scales much below the cutoff. We revisit $N$-flation and KKLT-type compactifications in this light, and show that they are perfectly consistent with the covariant entropy bound. Thus, while quantum gravity might yet spoil large field inflation, holographic considerations in the semiclassical theory do not obstruct it.