Scalar and Vector Field Constraints, Deflection of Light and Lensing in Modified Gravity (MOG)

Abstract

A conformal coupling of the metric in the Jordan frame to the energy-momentum tensor, screens the scalar field gravitational coupling strength $G$ in modified gravity (MOG). The scalar field acquires a mass which depends on the local matter density: the scalar field particle is massive for the Sun and earth, where the density is high compared to low density environments in cosmology and astrophysics. Together with the screening of the vector field $\phi_\mu$, this guarantees that solar system tests of gravity are satisfied. The conformal metric is coupled to the electromagnetic matter field and energy-momentum tensor, screening $G$ for the Sun and the deflection of light by the Sun and the Shapiro time delay in MOG are in agreement with general relativity. For galaxies and galactic clusters the enhanced gravitational coupling constant $G$ leads to agreement with gravitational lensing without dark matter. For compact binary pulsars the screening of $G$ removes the monopole and dipole gravitational radiation modes in agreement with the binary pulsar timing data.