Gravitational wave memory and its tail in cosmology

Abstract

We study gravitational wave memory effect in the FRW cosmological model with matter and cosmological constant. Since the background is curved, gravitational radiation develops a tail part arriving after the main signal that travels along the past light cone of the observer. First we discuss first order gravitational wave sourced by a binary system, and find that the tail only gives a negligible memory, in accord with previous results. Then we study the nonlinear memory effect coming from induced gravitational radiation sourced by first order gravitational radiation propagating over cosmological distances. In the light cone part of the induced gravitational wave we find a novel term missed in previous studies of the cosmological memory effect. Furthermore, we show that the induced gravitational wave has a tail part that slowly accumulates after the light cone part has passed and grows to a sizeable magnitude over a cosmological timescale. This tail part of the memory effect will be a new component in the stochastic gravitational wave background.

Curvature Dynamics in General Relativity

“…This may manifest itself in additional propagating degrees of freedom, as ∇ i E ij and ∇ i B j i receive contributions from the right-hand side of Equation (18). These corrections require additional study; they could show up, e.g., in gravitational memory effects in non-flat background geometries [5,10].…”

Cosmological memory effect in scalar-tensor theories

“…In our idealized case in which GWs are produced due to the particle-like sources with energy-momentum tensor (12), the memory effect is characterized by the "existence of first derivative of the delta functions" in the components of the Riemann tensor [23]. The electric components of the Riemann tensor up to the linear order in tensor and scalar perturbations (22) are given by…”

“…In the case of the cosmological spacetime, which is not asymptotically flat, characterizing the memory effect is more subtle. Recently, this issue was studied by different groups with different approaches [16][17][18][19][20][21][22] and among them, we will focus on the approach adopted by Tolish and Wald [23]. Indeed, using the fact that the spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime is conformally flat, they have developed a general setup to study memory effect which is applicable as far as an idealized particle-like source for GWs is considered.…”

Cosmological memory effect in scalar-tensor theories

“…In the case of the cosmological spacetime, which is not asymptotically flat, characterizing the memory effect is more subtle. Recently, this issue was studied by different groups with different approaches [16][17][18][19][20][21][22] and among them, we will focus on the approach adopted by Tolish and Wald [23]. Indeed, using the fact that the spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime is conformally flat, they have developed a general setup to study memory effect which is applicable as far as an idealized particle-like source for GWs is considered.…”