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

TL;DR

This paper explores gravitational radiation in quadratic $f(R)$ gravity, revealing modifications to the quadrupole formula and predicting additional multipole radiation due to an extra scalar degree of freedom.

Contribution

It derives leading order corrections to the quadrupole formula in $f(R)$ gravity and analyzes the implications of the scalar degree of freedom on gravitational radiation.

Findings

Derived corrections to the quadrupole formula in $f(R)$ gravity.

Predicted monopole and dipole gravitational radiation.

Estimated constraints on the parameter $a$ from binary pulsar data.

Abstract

We investigate the gravitational radiation emitted by an isolated system for gravity theories with Lagrange density $f(R) = R + aR^2$. 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 $a \lesssim 1.7\cdot10^{17}\,\mathrm{m}^2$ by constraining the dipole power to account at most for 1% of the quadrupole power as predicted by General Relativity.