  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.
