Gravitational waves in the presence of a cosmological constant

José Bernabeu, Domènec Espriu, and Daniel Puigdomènech
Phys. Rev. D 84, 063523 – Published 26 September 2011; Erratum Phys. Rev. D 86, 069904 (2012)

Abstract

We derive the effects of a nonzero cosmological constant Λ on gravitational wave propagation in the linearized approximation of general relativity. In this approximation, we consider the situation where the metric can be written as gμν=ημν+hμνΛ+hμνW, hμνΛ,W1, where hμνΛ is the background perturbation and hμνW is a modification interpretable as a gravitational wave. For Λ0, this linearization of Einstein equations is self-consistent only in certain coordinate systems. The cosmological Friedmann-Robertson-Walker coordinates do not belong to this class and the derived linearized solutions have to be reinterpreted in a coordinate system that is homogeneous and isotropic to make contact with observations. Plane waves in the linear theory acquire modifications of order Λ, both in the amplitude and the phase, when considered in Friedmann-Robertson-Walker coordinates. In the linearization process for hμν, we have also included terms of order O(Λhμν). For the background perturbation hμνΛ, the difference is very small, but when the term hμνWΛ is retained the equations of motion can be interpreted as describing massive spin-2 particles. However, the extra degrees of freedom can be approximately gauged away, coupling to matter sources with a strength proportional to the cosmological constant itself. Finally, we discuss the viability of detecting the modifications caused by the cosmological constant on the amplitude and phase of gravitational waves. In some cases, the distortion with respect to gravitational waves propagating in Minkowski space-time is considerable. The effect of Λ could have a detectable impact on pulsar timing arrays.

  • Figure
  • Received 23 June 2011

DOI:https://doi.org/10.1103/PhysRevD.84.063523

© 2011 American Physical Society

Erratum

Erratum: Gravitational waves in the presence of a cosmological constant [Phys. Rev. D 84, 063523 (2011)]

José Bernabeu, Domènec Espriu, and Daniel Puigdomènech
Phys. Rev. D 86, 069904 (2012)

Authors & Affiliations

José Bernabeu

  • Departament de Física Teòrica IFIC, Universitat de València-CSIC, Dr. Moliner 50, 46100 Burjassot, València, Spain

Domènec Espriu and Daniel Puigdomènech

  • Departament d’Estructura i Constituents de la Matèria, Institut de Ciències del Cosmos (ICCUB) Universitat de Barcelona, Martí i Franquès, 1, 08028 Barcelona, Spain

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Issue

Vol. 84, Iss. 6 — 15 September 2011

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