On Gravitational Radiation in Quadratic $f(R)$ Gravity

Abstract

We investigate the gravitational radiation emitted by an isolated system for gravity theories with Lagrange density $f(R)=R+a{R}^2$. As a formal result we obtain leading order corrections to the quadrupole formula in General Relativity. We make use of the analogy of $f(R)$ theories with scalar--tensor theories, which in contrast to General Relativity feature an additional scalar degree of freedom. Unlike General Relativity, where the leading order gravitational radiation is produced by quadrupole moments, the additional degree of freedom predicts gravitational radiation of all multipoles, in particular monopoles and dipoles, as this is the case for the most alternative gravity theories known today. An application to a hypothetical binary pulsar moving in a circular orbit yields the rough limit $a\lesssim 1.7\cdot 10^{17}{\mathrm{m}}^2$ by constraining the dipole power to account at most for 1% of the quadrupole power as predicted by General Relativity.

14 Pages, 1 Figure

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• Gravitational wave polarizations in nonminimally coupled gravity
• Impulsive gravitational waves of massless particles in extended theories of gravity
• Gravitational waves in massive Horndeski theory with a potential
• Propagation and emission of gravitational waves in the weak-field limit within the Palatini formalism
• Spherically Symmetric Potentials in Quadratic $f(R)$ Gravity