Constraints on modular inflation in supergravity and string theory

TL;DR

This paper analyzes the conditions under which slow-roll inflation can occur in string theory models, revealing a close relationship with metastable vacua and showing that viable inflation often requires specific compactification scenarios or corrections.

Contribution

It provides a general algebraic framework linking inflationary conditions to metastable vacua in supergravity and string models, with specific insights into Calabi-Yau compactifications.

Findings

Viable inflation depends on the ratio of inflation scale to gravitino mass.

Subleading corrections enable slow-roll inflation with suppressed inflationary scale.

Certain compactifications can support inflation with inflation scale exceeding the gravitino scale.

Abstract

We perform a general algebraic analysis on the possibility of realising slow-roll inflation in the moduli sector of string models. This problem turns out to be very closely related to the characterisation of models admitting metastable vacua with non-negative cosmological constant. In fact, we show that the condition for the existence of viable inflationary trajectories is a deformation of the condition for the existence of metastable de Sitter vacua. This condition depends on the ratio between the scale of inflation and the gravitino mass and becomes stronger as this parameter grows. After performing a general study within arbitrary supergravity models, we analyse the implications of our results in several examples. More concretely, in the case of heterotic and orientifold string compactifications on a Calabi-Yau in the large volume limit we show that there may exist fully viable models, allowing both for inflation and stabilisation. Additionally, we show that subleading corrections breaking the no-scale property shared by these models always allow for slow-roll inflation but with an inflationary scale suppressed with respect to the gravitino scale. A scale of inflation larger than the gravitino scale can also be achieved under more restrictive circumstances and only for certain types of compactifications.