Linearized f(R) gravity: gravitational radiation and solar system tests

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 + a 2 R 2 / 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 | a 2 | ≲ 1.2 × 10 18 m 2 . 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 10 6 M ⊙ black hole if | a 2 | ≳ 10 17 m 2 , 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 | a 2 | ≲ 2 × 10 − 9 m 2 . 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