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

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