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

We demonstrate that a broad class of modular inflation models predicts the emergence of new physics within an energy range of approximately ${10}^{15}\mathrm{G}\mathrm{e}\mathrm{V}$ to ${10}^{17}\mathrm{G}\mathrm{e}\mathrm{V}$. 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.