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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 $\dotω$ of binary pulsars in harmonic coordinates is given. After that, $\dotω$ 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 $α$ and $λ$. $α$ and $λ$ respectively represent the strength of the intermediate-range force coupling and its length scale. The limits from four binary pulsars data are respectively $λ=(4.95\pm0.02)\times10^{8}$m and $α=(2.30\pm0.01)\times10^{-8}$ if $β=1$ where $β$ is a parameter like standard parametrized post-Newtonian parameter $β_{PPN}$. When three degrees of freedom ($α$, $λ$ and $\barβ\equivβ-1$) in 1$σ$ confidence level are considered, it yields $α=(4.21\pm0.01)\times10^{-4}$, $λ=(4.51\pm0.01)\times10^{7}$m and $\barβ=(-3.30\pm0.01)\times10^{-3}$. Through our research on the scalar-tensor theory with the intermediate-range force, it shows that the parameter $α$ is directly related to the parameter $γ$ ($α=(1-γ)/(1+γ)$). Thus, this presents the constraints on $1-γ$ by binary pulsars which is about $10^{-4}$ for three degrees of freedom.