Modified scalar-tensor-vector gravity theory and the constraint on its parameters

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 [1]. However, two assumptions have been used: (i) B(r)=A^-1(r), where $B(r)$ and $A(r)$ are g₀₀ and gᵣᵣ 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 γ=1. In this paper, we relax these two assumptions and study STVG further by using the post-Newtonian approximation approach. With abandoning the assumptions, we find γ≠1 in general cases of STVG. Then, a version of modified STVG is proposed through introducing a coupling function of scalar field G: θ(G). We have derived the metric and equations of motion in 1PN for general matter without specific equation of state and N point masses firstly. Subsequently, the secular periastron precession ̇ ω of binary pulsars in harmonic coordinates is given. After discussing two parametrized post-Newtonian parameters (γ and β) and two Yukawa parameters (α and λ), we use ̇ ω of four binary pulsars data (PSR B1913+16, PSR B1534+12, PSR J0737-3039, and PSR B2127+11C) to constrain the Yukawa parameters for modified STVG: λ=(3.97±0.01)×10⁸ m and α=(2.40±0.02)×10^-8 if we fix |2γ-β-1|=0.