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.

arXiv comment14 Pages, 1 Figure

References in corpus (9)

• Chameleon Fields: Awaiting Surprises for Tests of Gravity in Space
• Linearized f(R) Gravity: Gravitational Radiation & Solar System Tests
• A bird's eye view of f(R)-gravity
• On the 1/c Expansion of f(R) Gravity
• Effective Gravitational Wave Stress-energy Tensor in Alternative Theories of Gravity
• The Parameterised Post-Newtonian Limit of Fourth-Order Theories of Gravity
• Massive relic gravitational waves from f(R) theories of gravity: production and potential detection
• Massive gravitational waves from the R^2 theory of gravity: production and response of interferometers
• An oscillating Universe from the linearized R^{2} theory of gravity

Cited by in corpus (27)

• Extended Theories of Gravity
• Testing General Relativity with Present and Future Astrophysical Observations
• Black Hole Based Tests of General Relativity
• Modified gravity with logarithmic curvature corrections and the structure of relativistic stars
• Neutrino coupling to cosmological background: A review on gravitational Baryo/Leptogenesis
• Testing f(R)-theories using the first time derivative of the orbital period of the binary pulsars
• Propagation of gravitational waves in teleparallel gravity theories
• Gravitational Waves in Viable f(R) Models
• Gravitational perturbations of a Kerr black hole in $f(R)$ gravity
• Probing the physical and mathematical structure of $f(R)$ gravity by PSR $J0348+0432$
• Pure double-layer bubbles in quadratic F(R) gravity
• Consequences of f(R)-theories of gravity on gravitational leptogenesis
• Neutron Stars in Modified Teleparallel Gravity
• Gravitational waves in higher-order $R^2$ gravity
• Gravitational waves from inspiraling black holes in quadratic gravity
• Monopolar and quadrupolar gravitational radiation from magnetically deformed neutron stars in modified gravity
• Scalar Mode Quadrupole Radiation from Astronomical Sources in $F(R)$ Modified Gravity
• Gravitational wave polarizations in nonminimally coupled gravity
• Multipole analysis for linearized $f(R,\mathcal{G})$ gravity with irreducible Cartesian tensors
• Impulsive gravitational waves of massless particles in extended theories of gravity
• Gravitational radiation in Infinite Derivative Gravity and connections to Effective Quantum Gravity
• Multipole analysis for linearized $f(R)$ gravity with irreducible Cartesian tensors
• Multipole analysis in the radiation field for linearized $f(R)$ gravity with irreducible Cartesian tensors
• Gravitational waves in massive Horndeski theory with a potential
• One-Dimensional Primordial Gravitational Waves In Pure Quadratic Gravity
• Propagation and emission of gravitational waves in the weak-field limit within the Palatini formalism
• Spherically Symmetric Potentials in Quadratic $f(R)$ Gravity