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Gravitational waves in the presence of a cosmological constant

Jun, 2011
20 pages
Published in:
  • Phys.Rev.D 84 (2011) 063523,
  • Phys.Rev.D 86 (2012) 069904 (erratum)
e-Print:
DOI:
Report number:
  • FTUV-11-2106,
  • UB-ECM-FP-55-11,
  • ICCUB-11-151
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Abstract: (arXiv)
We derive the effects of a non-zero cosmological constant Λ\Lambda 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+hμνWg_{\mu\nu}= \eta_{\mu\nu}+ h_{\mu\nu}^\Lambda + h_{\mu\nu}^W, hμνΛ,W<<1h_{\mu\nu}^{\Lambda,W}<< 1, where hμνΛh_{\mu\nu}^{\Lambda} is the background perturbation and hμνWh_{\mu\nu}^{W} is a modification interpretable as a gravitational wave. For Λ≠0\Lambda \neq 0 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\sqrt{\Lambda}, both in the amplitude and the phase, when considered in FRW coordinates. In the linearization process for hμνh_{\mu\nu}, we have also included terms of order O(Λhμν)\mathcal{O}(\Lambda h_{\mu\nu}). For the background perturbation hμνΛh_{\mu\nu}^\Lambda the difference is very small but when the term hμνWΛh_{\mu\nu}^{W}\Lambda 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\Lambda could have a detectable impact on pulsar timing arrays.
Note:
  • 20 pages, 1 figure
  • 04.30.-w
  • 98.80.Es
  • Einstein equation: linear
  • gravitational radiation: propagation
  • space-time: Robertson-Walker
  • spin: 2
  • pulsar: frequency
  • cosmological constant
  • space-time: de Sitter
  • solution: static
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