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 1. 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 approximation approach. With abandoning the assumptions, we find gamma not equal 1 in general cases of STVG. Then, a version of modified STVG is proposed through introducing a coupling function of scalar field G: theta(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 omega of binary pulsars in harmonic coordinates is given. After discussing two parametrized post-Newtonian parameters (gamma and beta) and two Yukawa parameters (alpha and lambda), we use 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 modified STVG: lambda=(3.97 +/- 0.01)x10(8) m and alpha=(2.40 +/- 0.02)x10(-8) if we fix |2 gamma-beta-1|=0.