Inflationary constraints on the moduli-dependent species scale in modular invariant theories

Abstract

We demonstrate that a broad class of modular inflation models predicts the emergence of new physics within an energy range of approximately \( 10^{15} \, \mathrm{GeV} \) to \( 10^{17} \, \mathrm{GeV} \). This prediction arises by comparing the moduli-dependent species scale with observational constraints on inflation. Specifically, we illustrate this within the context of \( SL(2, \mathbb{Z}) \)-modular inflation models by re-expressing inflationary observables in terms of the species scale. We further discuss the implications of this approach for generic Calabi-Yau threefolds.