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, showing that this reformulation allows us to directly constrain the fundamental parameters related to the geometry of extra dimensions, specifically the second Chern numbers.