A Field Range Bound for General Single-Field Inflation

TL;DR

The paper develops a universal framework for single-field inflation using the EFT of inflation and derives a generalized Lyth bound that links the observable tensor-to-scalar ratio $r$ to a physically meaningful field range defined by Planck-suppressed corrections to the Goldstone mode $\pi$. By analyzing the stress tensor and the scaling of fluctuations, it shows that a universal power-spectrum form arises with a symmetry-breaking scale $\Lambda_b$ and a scaling dimension $\Delta$, and it derives a robust NEC-based upper bound on $r$ at horizon crossing. The main result is a field-range bound, $\frac{\Lambda^2 \Delta t}{M_{pl}} \sim \sqrt{r}\, c_p^{-3/2}\, \Delta N$, which is at least as strong as the traditional Lyth bound and often stronger, implying that non-trivial dynamics cannot evade UV sensitivities in the gravity-wave signal. These findings have significant implications for the viability of small-field models and for connecting observable tensor modes to Planck-scale physics in UV-complete theories.

Abstract

We explore the consequences of a detection of primordial tensor fluctuations for general single-field models of inflation. Using the effective theory of inflation, we propose a generalization of the Lyth bound. Our bound applies to all single-field models with two-derivative kinetic terms for the scalar fluctuations and is always stronger than the corresponding bound for slow-roll models. This shows that non-trivial dynamics can't evade the Lyth bound. We also present a weaker, but completely universal bound that holds whenever the Null Energy Condition (NEC) is satisfied at horizon crossing.