Constraints on a scalar-tensor theory with an intermediate-range force by binary pulsars

Searching for an intermediate-range force has been considerable interests in gravity experiments. In this paper, aiming at a scalar-tensor theory with an intermediate-range force, we have derived the metric and equations of motion (EOMs) in the first post-Newtonian (1PN) approximation for general matter without specific equation of state and $N$ point masses firstly. Subsequently, the secular periastron precession $\dot{\omega}$ of binary pulsars in harmonic coordinates is given. After that, $\dot{\omega}$ of four binary pulsars data (PSR B1913+16, PSR B1534+12, PSR J0737-3039 and PSR B2127+11C) have been used to constrain the intermediate-range force, namely, the parameters $\alpha$ and $\lambda$. $\alpha$ and $\lambda$ respectively represent the strength of the intermediate-range force coupling and its length scale. The limits from four binary pulsars data are respectively $\lambda=(4.95\pm0.02)\times10^{8}$m and $\alpha=(2.30\pm0.01)\times10^{-8}$ if $\beta=1$ where $\beta$ is a parameter like standard parametrized post-Newtonian parameter $\beta_{PPN}$. When three degrees of freedom ($\alpha$, $\lambda$ and $\bar{\beta}\equiv\beta-1$) in 1$\sigma$ confidence level are considered, it yields $\alpha=(4.21\pm0.01)\times10^{-4}$, $\lambda=(4.51\pm0.01)\times10^{7}$m and $\bar{\beta}=(-3.30\pm0.01)\times10^{-3}$. Through our research on the scalar-tensor theory with the intermediate-range force, it shows that the parameter $\alpha$ is directly related to the parameter $\gamma$ ($\alpha=(1-\gamma)/(1+\gamma)$). Thus, this presents the constraints on $1-\gamma$ by binary pulsars which is about $10^{-4}$ for three degrees of freedom.