Gravitational memory and soft theorems: The local perspective

TL;DR

This paper explores the connection between gravitational memory effects, soft theorems, and residual gauge transformations in general relativity, providing new insights into their local descriptions and implications for cosmology.

Contribution

It establishes a local gauge perspective on gravitational memory, reproduces known soft theorems, and introduces new soft theorems for cosmological correlators.

Findings

Gravitational memory corresponds to residual diffeomorphisms in local gauges.

Reproduction of soft theorems for scattering amplitudes.

Derivation of new soft theorems for cosmological correlators.

Abstract

In general relativity, gravitational memory describes the lasting change in the separation and relative velocity of freely falling detectors after the passage of gravitational waves (GWs). In this paper, we elucidate the relation between Bondi-Metzner-Sachs transformations at future null infinity and the description of gravitational memory in local synchronous coordinates, commonly used in GW detectors like LISA. We show that gravitational memory corresponds to large residual diffeomorphisms in this gauge, such as volume-preserving spatial rescalings. We reproduce the associated soft theorems for scattering amplitudes. Finally, we derive novel soft theorems for equal-time (in-in) correlation functions, which are recognized as the flat space analogues of inflationary consistency relations with a soft tensor mode. These relations provide a pathway toward uncovering deeper connections between gravitational memory and cosmological correlators.