A species scale-driven breakdown of effective field theory in time-dependent string backgrounds

Abstract

We present a novel way in which effective field theory (EFT) can break down in cosmological string backgrounds depending on the behavior of the quantum gravity cutoff in infinite distance limits, known as the species scale $Λ_s$. Namely, EFT can break down if the species scale $Λ_s$ falls off so rapidly as the Friedmann-Robertson-Walker (FRW) scale factor grows from some initial value $a_i$ to some final value $a_f$ that the physical momentum of an initial Hubble-sized perturbation $\sim H_i^{-1}$ grows to exceed the species scale. For EFT to remain valid, a new condition $H_i \frac{a_i}{a_f} \ll Λ_{s,f}$ must hold, which is distinct from Trans-Planckian conditions discussed in the literature. Using the universal relation $\frac{\nabla m}{m} \cdot \frac{\nabla Λ_s}{Λ_s} = \frac{1}{d-2}$ in the infinite distance limits of moduli space where $m$ is the mass scale of the lightest tower and $\nabla$ measures variations with respect to the canonical metric on moduli space, we show that spatially flat FRW solutions in the string landscape violate this condition or at best marginally satisfy it. However, we find that sufficiently large negative spatial curvature always avoids a breakdown. To avoid EFT breakdown, we derive an upper bound on the duration of quasi-de Sitter expansion that classically evolves to decelerated expansion. Our bound is proportional to the Trans-Planckian Censorship Conjecture (TCC) bound, with the advantage that it applies to any FRW solution in the string landscape. Finally, we distinguish EFT breakdown from TCC violation, the latter being a quantum gravity constraint rather than an EFT limitation. Perhaps our most surprising finding is that in any flat FRW solution that develops a weakly coupled string at future infinity the EFT inevitably breaks down.