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

TL;DR

This paper derives equations for a scalar-tensor gravity theory with an intermediate-range force and uses binary pulsar data to constrain the force's strength and length scale, providing new limits on deviations from general relativity.

Contribution

It presents the first derivation of metric and equations of motion in 1PN approximation for this theory and constrains force parameters using pulsar observations.

Findings

Constraints on force length scale: $oxed{(4.95 ext{ to }4.51) imes10^{7} ext{ m}}$

Constraints on force strength: $oxed{(2.30 ext{ to }4.21) imes10^{-8}}$

Limits on deviation from GR: $1-oxed{ ext{gamma}} ext{ about }10^{-4}$

Abstract

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.