Updated constraints on modified gravity from binary pulsars

Binary pulsars offer a unique natural laboratory to test General Relativity (GR) and probe for deviations from its paradigm, as predicted by alternative theories of gravity. In this paper, we study two such possible deviations: a time variation of Newton's constant $G$ and the emission of dipolar gravitational radiation. We use updated data for some well-known pulsars, namely PSR J1738+0333, PSR J1012+5307, and PSR J1713+0747, to extract the Keplerian and post-Keplerian parameters that characterize their orbital dynamics, using recent high-precision pulsar timing data and a Bayesian parameter estimation with Markov chain Monte Carlo (MCMC) techniques. We do this via the TEMPO2 software, the MCMC4Tempo2 plugin, and a unified python pipeline to analyze the data. We then perform a combined analysis of different binary systems to constrain both the time evolution of Newton's constant and the dipolar emission parameter $\kappa_D$. For the best of our three pulsars (PSR J1713+0747), we obtain $\dot{G}/G = (0.32 \pm 0.31) \times 10^{-12}~\text{yr}^{-1}$ at 95\% confidence, along with a stringent constraint on the dipolar emission parameter, $\kappa_D = (-0.04 \pm 0.14) \times 10^{-4}$. Thanks to the recent high-precision timing data sets, we provide updated bounds on key parameters relevant to modified gravity theories, and we find that our results are consistent with GR.