Gravitational wave memory and its tail in cosmology

Abstract

We study gravitational wave memory effect in the Friedmann-Robertson-Walker cosmological model with matter and a 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 we 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.

Persistent gravitational wave observables: Curve deviation in asymptotically flat spacetimes

“…• perturbations off of a known, exact spacetime (considered for flat backgrounds in Paper I and, for example, [13,[19][20][21], and for cosmological backgrounds in, for example, [22][23][24]);…”

On the gravitational precession memory effect for an ensemble of gyroscopes

“…As a pulse of gravitational wave passes through the box and disturb the falling trajectory, the partition function of this ensemble would experience a change because of change in the Hamiltonian of the system. We saw that this change of the thermodynamic properties is proportional to the precession memory effect factor ∆Φ, equation (11).…”

“…The displacement memory effect [7,8], the most known one, emerges as a net displacement between freely falling test particles in the wave zone. There are other effects such as kick memory [9,10], spin memory [11][12][13], center-of-mass memory [14], and gyroscopic memory [15][16][17] appearing in different contexts.…”

Inflationary gravitational wave background as a tail effect

“…The main signal arrives on the light cone and is theoretically well understood [27]. The corresponding tail has not yet been observed, but its magnitude has been computed [24] (see also Refs. [19][20][21][22][23]).…”