Constraints on modular inflation in supergravity and string theory

TL;DR

The paper analyzes whether slow-roll inflation can be realized in the moduli sector of string-inspired supergravity theories. It derives a curvature-based bound on the slow-roll parameter eta that hinges on the Goldstino direction and the ratio gamma = V/(3 m_{3/2}^2), showing that the inflation viability condition is a deformation of the metastable de Sitter vacuum condition. Through general analysis and concrete Calabi-Yau examples, it demonstrates that high-scale inflation (gamma >> 1) is generally hard unless the Kähler geometry allows large hat_sigma or subleading corrections break no-scale symmetry; uplifting sectors can modify the bound but often only enable inflation at scales below the gravitino mass. The work links the possibility of modular inflation directly to the geometry of the moduli space, offering explicit criteria for heterotic, Type II orientifold, and Calabi-Yau compactifications. Subleading corrections and uplifting mechanisms emerge as potential routes to realize inflation, but typically at reduced scales unless exceptional curvature properties are present.

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.