Inflationary Adler Conditions

TL;DR

This paper derives a new soft theorem related to the spontaneous breaking of Lorentz boosts during inflation, connecting Goldstone boson emissions to Lorentz boost transformations in flat-space scattering amplitudes.

Contribution

It introduces a novel soft theorem for Lorentz boost breaking in inflation, linking Goldstone boson emissions to non-relativistic boost transformations, and identifies Dirac-Born-Infeld Inflation as uniquely compatible with emergent Lorentz invariance.

Findings

Derived a soft theorem for Lorentz boost breaking during inflation.

Linked Goldstone boson emission to Lorentz boost transformations.

Identified Dirac-Born-Infeld Inflation as the unique theory with emergent Lorentz invariance.

Abstract

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.