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

By C. Berry, Jonathan R. Gair. 2011

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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 $f(R)=R+{a}_{2}{R}^{2}/2+\dots{}$. 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 $\ensuremath{\gamma}=1$. We find that planetary precession rates are enhanced relative to general relativity; from the orbit of Mercury we derive the bound $|{a}_{2}|\ensuremath{\lesssim}1.2\ifmmode\times\else\texttimes\fi{}{10}^{18}\text{ }\text{ }{\mathrm{m}}^{2}$. 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 ${10}^{6}{M}_{\ensuremath{\bigodot}}$ black hole if $|{a}_{2}|\ensuremath{\gtrsim}{10}^{17}{\mathrm{m}}^{2}$, assuming that the weak-field metric of the black hole coincides with that of a point mass. However E\"ot-Wash experiments provide the strictest bound $|{a}_{2}|\ensuremath{\lesssim}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}\text{ }\text{ }{\mathrm{m}}^{2}$. 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/de1ac952db4a99c52d841114eaed0409e3fb554d

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In Astronomy and Astrophysics

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In Nuclear and High Energy Physics

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