Locality in effective field theory for inflationary soft modes

TL;DR

This paper establishes a locality condition on the quantum state during inflation, ensuring local soft-mode dynamics, suppressing loop corrections, and guaranteeing infrared regularity, thereby unifying several key aspects of inflationary effective theory.

Contribution

It formulates a locality condition on the quantum state that unifies the understanding of soft modes, loop corrections, and infrared regularity in inflationary effective field theory.

Findings

Locality condition ensures soft-mode dynamics remain local.

Loop corrections from hard modes are perturbatively suppressed.

Infrared divergences are absent under the locality condition.

Abstract

The gradient expansion and the separate universe approach provide an effective description of inflationary soft modes after coarse-graining shorter-wavelength degrees of freedom. We formulate a locality condition on the quantum state, requiring that the hard-mode state in each local universe depend on the soft modes only through the local soft-mode values in the same patch. When this condition is satisfied, the coarse-grained soft-mode dynamics remains local, and loop corrections from hard modes to superhorizon correlators of the adiabatic curvature perturbation are perturbatively suppressed. This provides a model-independent diagnosis of when enhanced corrections due to hard modes can invalidate the gradient expansion. We further show that the same locality condition implies a generalized soft theorem, from which the standard consistency relations follow under additional assumptions. This formulation clarifies the origin of possible deviations from the standard consistency relations in multi-field systems or in a non-attractor background. We also show that the locality condition guarantees the absence of infrared divergences for the correlators of operators invariant under a large gauge transformation. Thus, locality of the hard-mode state provides a unified criterion for the effective description of inflationary soft modes, generalized soft theorems, the suppression of hard-mode loop corrections, and the infrared regularity of observable correlators.