Linearized f(R) gravity: Gravitational radiation and Solar System tests

Christopher Philip Luke Berry*, Jonathan R. Gair

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

125 Scopus citations


We investigate the linearized form of metric f(R)-gravity, assuming that f(R) is analytic about R=0 so it may be expanded as f(R)=R+a2R2/ 2+⋯ Gravitational radiation is modified, admitting an extra mode of oscillation, that of the Ricci scalar. We derive an effective energy-momentum tensor for the radiation. We also present weak-field metrics for simple sources. These are distinct from the equivalent Kerr (or Schwarzschild) forms. We apply the metrics to tests that could constrain f(R). We show that light deflection experiments cannot distinguish f(R)-gravity from general relativity as both have an effective post-Newtonian parameter γ=1. We find that planetary precession rates are enhanced relative to general relativity; from the orbit of Mercury we derive the bound |a2|1.2×1018m2. Gravitational-wave astronomy may be more useful: considering the phase of a gravitational waveform we estimate deviations from general relativity could be measurable for an extreme-mass-ratio inspiral about a 106M black hole if |a 2|1017m2, assuming that the weak-field metric of the black hole coincides with that of a point mass. However Eöt-Wash experiments provide the strictest bound |a2|2×10-9m2. Although the astronomical bounds are weaker, they are still of interest in the case that the effective form of f(R) is modified in different regions, perhaps through the chameleon mechanism. Assuming the laboratory bound is universal, we conclude that the propagating Ricci scalar mode cannot be excited by astrophysical sources.

Original languageEnglish (US)
Article number104022
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number10
StatePublished - May 11 2011

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)


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