Linearized f(R) gravity: Gravitational radiation and Solar System tests
Abstract
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 energymomentum tensor for the radiation. We also present weakfield 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 postNewtonian 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}. Gravitationalwave astronomy may be more useful: considering the phase of a gravitational waveform we estimate deviations from general relativity could be measurable for an extrememassratio inspiral about a 10^{6}M_{☉} black hole if a_{2}≳10^{17}m^{2}, assuming that the weakfield metric of the black hole coincides with that of a point mass. However EötWash 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.
 Publication:

Physical Review D
 Pub Date:
 May 2011
 DOI:
 10.1103/PhysRevD.83.104022
 arXiv:
 arXiv:1104.0819
 Bibcode:
 2011PhRvD..83j4022B
 Keywords:

 04.50.Kd;
 04.25.Nx;
 04.30.w;
 04.70.s;
 Modified theories of gravity;
 PostNewtonian approximation;
 perturbation theory;
 related approximations;
 Gravitational waves: theory;
 Physics of black holes;
 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Extragalactic Astrophysics;
 Astrophysics  High Energy Astrophysical Phenomena
 EPrint:
 19 pages, 1 figure