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'(R 0)-1 (where R 0 is the scalar curvature of the Universe at the present epoch) from the Tsujikawa model, i.e |f'(R 0)-1| < 2.09 × 10-4. This bound is stronger than those from most of the astrophysical observations and even some cosmological observations.

Dark energy as a critical period in binary motion: Bounds from multi-scale binaries

“…Therefore, they are useful tools for testing gravity due to the extreme precision of the radio pulses they emit. For instance, post-Keplerian parameters which take different forms in different theories of gravity have been constrained from pulsar measurements (Liu et al 2018;De Laurentis & Capozziello 2011;De Laurentis & De Martino 2014, 2015, 2014Dyadina et al 2016;Narang et al 2023; 4)) sets the scale above which dark energy dominates over gravity. For systems with β ≤ 1, the post-Newtonian correction to general relativistic effects can be observed.…”