Stringent Pulsar Timing Bounds on Light Scalar Couplings to Matter

Pulsar timing constraints on scalar-tensor theories with conformal and disformal couplings to matter are discussed. Reducing the dynamics to the motion in the center-of-mass frame and using the mean anomaly parametrization, we find the first post-Newtonian corrections induced by the conformal and disformal interactions in the form of a generalized quasi-Keplerian solution. We also derive the radiation reaction force due to scalar radiation and the corresponding post-Keplerian parameters (PKP). We use different pulsar time of arrival (TOA) datasets to probe the scalar corrections to the PKP. In particular, we focus on systems with large orbital frequencies as the contributions to the PKP terms induced by the disformal coupling are sensitive to higher frequencies. We find that the most constraining pulsar timings are PSR <math display="inline"><mrow><mi mathvariant="normal">B</mi><mn>1913</mn><mo>+</mo><mn>16</mn></mrow></math> and the double pulsar PSR J0737-3039A/B, being of the order of the Cassini bound on the conformal coupling obtained from the Shapiro effect in the solar system. The combined constraints using other pulsar timings give an upper bound on the conformal coupling <math display="inline"><msup><mi>β</mi><mn>2</mn></msup><mo>&lt;</mo><mn>2.33</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>5</mn></mrow></msup></math> and a lower bound on the disformal coupling scale of <math display="inline"><mi mathvariant="normal">Λ</mi><mo>≥</mo><mn>1.12</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> which is comparable to the Cassini bound and to the GW-170817 constraints respectively. Future measurements for pulsar timing with black hole companions are also discussed.