Modular invariant inflation

TL;DR

This paper explores how modular invariance in string theory constrains inflation models, favoring small field inflation with specific potential shapes and suggesting ways to test these models through reheating signatures.

Contribution

It demonstrates that modular invariance restricts inflationary potentials, making large field models unlikely and providing a framework for small field inflation consistent with string theory symmetries.

Findings

Large field inflation models are disfavored under modular invariance.

Small field inflation models can be realized with a potential similar to hilltop inflation.

Primordial gravitational waves are difficult to detect in this setup, but reheating signatures may help falsify the model.

Abstract

Modular invariance is a striking symmetry in string theory, which may keep stringy corrections under control. In this paper, we investigate a phenomenological consequence of the modular invariance, assuming that this symmetry is preserved as well as in a four dimensional (4D) low energy effective field theory. As a concrete setup, we consider a modulus field $T$ whose contribution in the 4D effective field theory remains invariant under the modular transformation and study inflation drived by $T$. The modular invariance restricts a possible form of the scalar potenntial. As a result, large field models of inflation are hardly realized. Meanwhile, a small field model of inflation can be still accomodated in this restricted setup. The scalar potential traced during the slow-roll inflation mimics the hilltop potential $V_{ht}$, but it also has a non-negligible deviation from $V_{ht}$. Detecting the primordial gravitational waves predicted in this model is rather challenging. Yet, we argue that it may be still possible to falsify this model by combining the information in the reheating process which can be determined self-completely in this setup.