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Inflationary Adler Conditions

We derive a new soft theorem that corresponds to the spontaneous breaking of Lorentz boosts. This is motivated by the dynamics of inﬂation in the sub-horizon (ﬂat-space) limit, where spacetime becomes ﬂat but Lorentz boosts are still broken. In this limit, the scattering amplitudes become sensible observables. We relate the soft emission of a Goldstone boson to the (non-relativistic) Lorentz boost of the hard scattering amplitudes. This is the on-shell avatar of the spontaneous breaking of Lorentz boosts, analogous to the Adler zero of pions in the chiral symmetry breaking. We comment on several applications to inﬂation, including the demonstration that Dirac-Born-Infeld Inﬂation is the unique theory that has an emergent Lorentz invariance when the boosts are spontaneously broken.