Gravitational radiation from binary systems in $f(R)$ gravity: A semi-classical approach

Abstract

The rate of energy loss and orbital period decay of quasi-stable compact binary systems are derived in $f(R)$ theory of gravity using the method of a single vertex graviton emission process from a classical source. After linearising the $f(R)$ action written in an equivalent scalar-tensor format in the Einstein frame, we identify the appropriate interaction terms between the massless spin-2 tensor mode, massive scalar mode, and the energy momentum tensor. The definition of the scalar field is related to the $f(R)$ models. Then using the interaction vertex we compute the rate of energy loss due to spin-2 quadrupole radiation, which comes out to be the same as the Peter-Mathews formula with a multiplication factor, and also the energy loss due to the scalar dipole radiation. The total energy loss is the sum of these two contributions. Our derivation is most general as it is applicable for both arbitrary eccentricity of the binary orbits and arbitrary mass of the scalar field. Using the derived theoretical formula for the period decay of the binary systems, we compare the predictions of $f(R)$ gravity and general relativity for the observations of four binary systems, i.e. Hulse-Taylor Binary, PSR J1141-6545, PSR J1738+0333, and PSR J0348+0432. Thus we put bound on three well-known $f(R)$ dark energy models, namely the Hu-Sawicki, the Starobinsky, and the Tsujikawa model. We get the best constraint on $f^{\prime }(R_0)-1$ (where $R_0$ is the scalar curvature of the Universe at the present epoch) from the Tsujikawa model, i.e $|f^{\prime }(R_0)-1|<2.09\times 10^{-4}$. This bound is stronger than those from most of the astrophysical observations and even some cosmological observations.

21 pages, 1 figure, 2 tables. Matched with published version

References in corpus (24)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• The Confrontation between General Relativity and Experiment
• A Massive Pulsar in a Compact Relativistic Binary
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Disappearing cosmological constant in f(R) gravity
• Beyond the Cosmological Standard Model
• Tests of general relativity from timing the double pulsar
• Modified f(R) gravity consistent with realistic cosmology: from matter dominated epoch to dark energy universe
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• The relativistic pulsar-white dwarf binary PSR J1738+0333 II. The most stringent test of scalar-tensor gravity
• The Large Scale Structure of f(R) Gravity
• Modified f(R) gravity unifying R^m inflation with \LambdaCDM epoch
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• Matter instability in modified gravity
• Solar System tests DO rule out 1/R gravity
• Stability of Cosmological Solution in f(R) Models of Gravity
• Cluster Constraints on f(R) Gravity
• Cosmological Constraints on f(R) Acceleration Models
• Gravitational-radiation losses from the pulsar-white-dwarf binary PSR J1141-6545
• Constraining f(R) gravity in solar system, cosmology and binary pulsar systems
• On the current status of Modified Gravity
• Constraint on $f(R)$ Gravity through the Redshift Space Distortion
• Study of eccentric binaries in Horndeski theory

Cited by in corpus (5)

• Radiative losses and radiation-reaction effects at the first post-Newtonian order in Einstein-Cartan theory
• Dark Energy as a Critical Period in Binary Motion: Bounds from Multi-scale Binaries
• Scalar Mode Quadrupole Radiation from Astronomical Sources in $F(R)$ Modified Gravity
• Graviton Mass Bounds in Very Special Relativity from Binary Pulsar's Gravitational Waves
• Gravitational radiation from binary systems in Unimodular gravity