Binary Pulsar constraints on massless scalar-tensor theories using Bayesian statistics

Binary pulsars provide some of the tightest current constraints on modified theories of gravity and these constraints will only get tighter as radio astronomers continue timing these systems. These binary pulsars are particularly good at constraining scalar-tensor theories in which gravity is mediated by a scalar field in addition to the metric tensor. Scalar-tensor theories can predict large deviations from General Relativity due to the fact that they allow for violation of the strong-equivalence principle through a phenomenon known as scalarization. This effect appears directly in the timing model for binary pulsars, and as such, it can be tightly constrained through precise timing. In this paper, we investigate these constraints for two scalar-tensor theories and a large set of realistic equations of state. We calculate the constraints that can be placed by saturating the current $1\sigma$ bounds on single post-Keplerian parameters, as well as employing Bayesian methods through Markov-Chain-Monte-Carlo simulations to explore the constraints that can be achieved when one considers all measured parameters simultaneously. Our results demonstrate that both methods are able to place similar constraints and that they are both indeed dominated by the measurements of the orbital period decay. The Bayesian approach, however, allows one to simultaneously explore the posterior distributions of not only the theory parameters but of the masses as well.