A Modified Scalar-Tensor-Vector Gravity Theory and the Constraint on its Parameters

Abstract

A gravity theory called scalar-tensor-vector gravity (STVG) has been recently developed and succeeded in solar system, astrophysical and cosmological scales without dark matter [J. W. Moffat, J. Cosmol. Astropart. Phys. 03, 004 (2006)]. However, two assumptions have been used: (i) $B(r)=A^{-1}(r)$, where $B(r)$ and $A(r)$ are $g_{00}$ and $g_{rr}$ in the Schwarzschild coordinates (static and spherically symmetric); (ii) scalar field $G=Const.$ in the solar system. These two assumptions actually imply that the standard parametrized post-Newtonian parameter $\gamma =1$. In this paper, we relax these two assumptions and study STVG further by using the post-Newtonian (PN) approximation approach. With abandoning the assumptions, we find $\gamma \ne 1$ in general cases of STVG. Then, a version of modified STVG (MSTVG) is proposed through introducing a coupling function of scalar field G: $\theta (G)$. We have derived the metric and equations of motion (EOM) in 1PN 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 discussing two PPN parameters ($\gamma$ and $\beta$) and two Yukawa parameters ($\alpha$ and $\lambda$), we use $\dot{\omega }$ of four binary pulsars data (PSR B1913+16, PSR B1534+12, PSR J0737-3039 and PSR B2127+11C) to constrain the Yukawa parameters for MSTVG: $\lambda =(3.97\pm 0.01)\times 10^8$m and $\alpha =(2.40\pm 0.02)\times 10^{-8}$ if we fix $|2\gamma -\beta -1|=0$.

39 pages, 4 figures, accepted by PRD

References in corpus (6)

• Tests of general relativity from timing the double pulsar
• The Bullet Cluster 1E0657-558 evidence shows Modified Gravity in the absence of Dark Matter
• Testing modified gravity with globular cluster velocity dispersions
• Constraints on the range lambda of Yukawa-like modifications to the Newtonian inverse-square law of gravitation from Solar System planetary motions
• Second post-Newtonian approximation of Einstein-aether theory
• Post-Newtonian parameters in the tensor-vector-scalar theory