Gravitational radiation from compact binary systems in the massive Brans-Dicke theory of gravity

TL;DR

This work analyzes gravitational radiation and related weak-field phenomenology in a Brans–Dicke theory with a massive scalar, deriving the PN expansions, Shapiro delay, Nordtvedt effect, and both tensor and scalar radiation for quasicircular binaries. The authors express the Yukawa-modified potentials via parameters ξ, γ, and α, and provide limiting behaviors that recover massless Brans–Dicke or General Relativity. By confronting the theory with Cassini Shapiro delay, Lunar Laser Ranging, and WD–NS binary observations (notably PSR J1012+5307 and PSR J1141-6545), they obtain competitive constraints on the Brans–Dicke coupling ω_BD and the scalar mass m_s, with Cassini yielding the strongest bounds for light scalars (ω_BD > 4×10^4 for m_s < 2.5×10^{-20} eV). The results highlight the sensitivity of Solar System and binary-pulsar tests to scalar-tensor modifications and outline paths for extending the analysis to eccentric or spinning binaries and more general scalar potentials. Overall, the paper quantifies how a massive scalar alters gravitational radiation and related observables, and translates those effects into stringent empirical constraints on alternative theories of gravity.

Abstract

We derive the equations of motion, the periastron shift, and the gravitational radiation damping for quasicircular compact binaries in a massive variant of the Brans-Dicke theory of gravity. We also study the Shapiro time delay and the Nordtvedt effect in this theory. By comparing with recent observational data, we put bounds on the two parameters of the theory: the Brans-Dicke coupling parameter ω_{BD} and the scalar mass m_s. We find that the most stringent bounds come from Cassini measurements of the Shapiro time delay in the Solar System, that yield a lower bound ω_{BD}>40000 for scalar masses m_s<2.5x10^{-20} eV, to 95% confidence. In comparison, observations of the Nordtvedt effect using Lunar Laser Ranging (LLR) experiments yield ω_{BD}>1000 for m_s<2.5x10^{-20} eV. Observations of the orbital period derivative of the quasicircular white dwarf-neutron star binary PSR J1012+5307 yield ω_{BD}>1250 for m_s<10^{-20} eV. A first estimate suggests that bounds comparable to the Shapiro time delay may come from observations of radiation damping in the eccentric white dwarf-neutron star binary PSR J1141-6545, but a quantitative prediction requires the extension of our work to eccentric orbits.

Figures (2)

• Figure 1: Left: Lower bound on $(\omega_{\rm BD}+3/2)$ as a function of the mass of the scalar $m_s$ from the Cassini mission data (black solid line; cf. Perivolaropoulos:2009ak), period derivative observations of PSR J1141-6545 (dashed red line) and PSR J1012+5307 (dot-dashed green line), and Lunar Laser Ranging experiments (dotted blue line). Vertical lines indicate the masses corresponding to the typical radii of the systems: 1AU (black solid line) and the orbital radii of the two binaries (dashed red and dot-dashed green lines). Right panel: upper bound on $\xi$ as a function of $m_s$. Linestyles are the same as in the left panel. Note that the theoretical bounds on the coupling parameters are $\omega>-3/2$ and $\xi<2$.
• Figure 2: Deformed integration contour $C_1+C_2+C_3+C_4$ along lines of steepest descent for $\rho(u)=iR(\omega u-m_s\sqrt{u^2-1})+i3\pi/4$ (corresponding to $n_1=+1,\;n_2=-1$) on the two sheets of the Riemann surface associated with $\sqrt{u^2-1}$. Here only the saddle point on the negative imaginary axis contributes.