Gravitational Radiation in Generalized Brans Dicke Theory: Compact Binary Systems

Abstract: This paper investigates the generation and properties of gravitational radiation within the framework of Generalized Brans-Dicke (GBD) theory, with a specific emphasis on its manifestation in compact binary systems. The primary focus of this study lies in the comprehensive exploration of gravitational radiation generated by compact binaries. The energy momentum tensor and the associated gravitational wave (GW) radiation power in GBD theory are investigated, elucidating the relationship between these fundamental concepts. Furthermore, detailed calculations are provided for the GW radiation power originating from both tensor fields and scalar fields. Based on our calculations, both scalar fields contribute to GW radiation by producing dipole radiation. We also study the period derivative of compact binaries in this theory. By comparing with the observational data of the orbital period derivative of the quasicircular white dwarf-neutron star binary PSR J1012+5307, we put bounds on the two parameters of the theory: the Brans-Dicke coupling parameter $\omega_{0}$ and the mass of geometrical scalar field $m_f$, \textcolor{black}{resulting in a lower bound $\omega_{0}>6.09723\times10^6$ for a massless BD scalar field and the geometrical field whose mass is smaller than $10^{-29} \text{GeV}$. The obtained bound on $\omega_0$ is two orders of magnitude stricter than those derived from solar system data.} Finally, we find the phase shift that GWs experience in the frequency domain during their propagation.