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The Cosmological Memory Effect

Alexander Tolish, Robert M. Wald

TL;DR

This work extends the gravitational memory effect to a spatially flat FLRW cosmology by modeling radiation from idealized point-particle sources and performing a gauge-invariant SVT decomposition. It shows that memory arises exclusively from tensor perturbations, with scalar and vector contributions ignorably smooth near the source event; the tensor memory is determined by the scale factor at emission and observation, independent of the detailed expansion history. A key result is that, when compared at the same luminosity distance, the memory in FLRW is enhanced by a factor of $(1+z)$ relative to Minkowski space, while tail effects modify waveforms but not the memory jump. The findings relate FLRW memory to the Minkowski case via a conformal mapping and provide a robust local definition of memory applicable beyond asymptotically flat spacetimes.

Abstract

The "memory effect" is the permanent change in the relative separation of test particles resulting from the passage of gravitational radiation. We investigate the memory effect for a general, spatially flat FLRW cosmology by considering the radiation associated with emission events involving particle-like sources. We find that if the resulting perturbation is decomposed into scalar, vector, and tensor parts, only the tensor part contributes to memory. Furthermore, the tensor contribution to memory depends only on the cosmological scale factor at the source and observation events, not on the detailed expansion history of the universe. In particular, for sources at the same luminosity distance, the memory effect in a spatially flat FLRW spacetime is enhanced over the Minkowski case by a factor of $(1 + z)$.

The Cosmological Memory Effect

TL;DR

This work extends the gravitational memory effect to a spatially flat FLRW cosmology by modeling radiation from idealized point-particle sources and performing a gauge-invariant SVT decomposition. It shows that memory arises exclusively from tensor perturbations, with scalar and vector contributions ignorably smooth near the source event; the tensor memory is determined by the scale factor at emission and observation, independent of the detailed expansion history. A key result is that, when compared at the same luminosity distance, the memory in FLRW is enhanced by a factor of relative to Minkowski space, while tail effects modify waveforms but not the memory jump. The findings relate FLRW memory to the Minkowski case via a conformal mapping and provide a robust local definition of memory applicable beyond asymptotically flat spacetimes.

Abstract

The "memory effect" is the permanent change in the relative separation of test particles resulting from the passage of gravitational radiation. We investigate the memory effect for a general, spatially flat FLRW cosmology by considering the radiation associated with emission events involving particle-like sources. We find that if the resulting perturbation is decomposed into scalar, vector, and tensor parts, only the tensor part contributes to memory. Furthermore, the tensor contribution to memory depends only on the cosmological scale factor at the source and observation events, not on the detailed expansion history of the universe. In particular, for sources at the same luminosity distance, the memory effect in a spatially flat FLRW spacetime is enhanced over the Minkowski case by a factor of .

Paper Structure

This paper contains 5 sections, 54 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Particle Sources
  3. Perturbation Theory in Cosmological Spacetimes
  4. The Retarded Gravitational Field and the Memory Effect
  5. Acoustic Shock Waves and Metric Continuity

Figures (1)

  • Figure 1: A spacetime diagram of the sort of gravitational wave source we will consider. Here $5$ point particles enter a single "source event" $q$, and $3$ emerge. The worldlines of the incoming and outgoing particles must be timelike or null geodesics.