The relativistic pulsar-white dwarf binary PSR J1738+0333 II. The most stringent test of scalar-tensor gravity

(abridged) We report the results of a 10-year timing campaign on PSR J1738+0333, a 5.85-ms pulsar in a low-eccentricity 8.5-hour orbit with a low-mass white dwarf companion (...) The measurements of proper motion and parallax allow for a precise subtraction of the kinematic contribution to the observed orbital decay; this results in a significant measurement of the intrinsic orbital decay: (-25.9 +/- 3.2) \times 10^{-15} s/s. This is consistent with the orbital decay from the emission of gravitational waves predicted by general relativity, (-27.7 +1.5/-1.9) \times 10^{-15} s/s (...). This agreement introduces a tight upper limit on dipolar gravitational wave emission, a prediction of most alternative theories of gravity for asymmetric binary systems such as this. We use this limit to derive the most stringent constraints ever on a wide class of gravity theories, where gravity involves a scalar field contribution. When considering general scalar-tensor theories of gravity, our new bounds are more stringent than the best current solar-system limits over most of the parameter space, and constrain the matter-scalar coupling constant α_0^2 to be below the 10^{-5} level. For the special case of the Jordan-Fierz-Brans-Dicke, we obtain the one-sigma bound α_0^2 < 2 \times 10^{-5}, which is within a factor two of the Cassini limit. We also use our limit on dipolar gravitational wave emission to constrain a wide class of theories of gravity which are based on a generalization of Bekenstein's Tensor-Vector-Scalar gravity (TeVeS), a relativistic formulation of Modified Newtonian Dynamics (MOND).