A field range bound for general single-field inflation

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 that applies to models of inflation coupled to Einstein gravity. Our strongest 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 of the inflaton can't evade the Lyth bound. We also present a weaker, but more universal bound that holds when the Null Energy Condition (NEC) is satisfied at horizon crossing.