Late time tails and nonlinear memories in asymptotically de Sitter spacetimes

TL;DR

This paper investigates how massless scalar waves behave in de Sitter spacetime with a central mass, revealing non-decaying tails and nonlinear memory effects that differ from flat spacetime predictions.

Contribution

It demonstrates the existence of linear and nonlinear tail-induced memories in scalar propagation within asymptotically de Sitter spacetimes, highlighting differences from flat spacetime behavior.

Findings

Scalar field amplitude approaches a constant at late times.

Nonlinear interactions amplify the scalar signal at null infinity.

Presence of tail-induced memory effects in de Sitter spacetime.

Abstract

We study the propagation of a massless scalar wave in de Sitter spacetime perturbed by an arbitrary central mass. By focusing on the late time limit, this probes the portion of the scalar signal traveling inside the null cone. Unlike in asymptotically flat spacetimes, the amplitude of the scalar field detected by an observer at timelike infinity does not decay back to zero but develops a spacetime constant shift - both at zeroth and first order in the central mass M. This indicates that massless scalar field propagation in asymptotically de Sitter spacetimes exhibits both linear and nonlinear tail-induced memories. On the other hand, for sufficiently late retarded times, the monopole portion of the scalar signal measured at null infinity is found to be amplified relative to its timelike infinity counterpart, by its nonlinear interactions with the gravitation field at first order in M.