We review and extend the Gauge Vectors-Tensor gravity: a covariant theory of gravity composed of a metric and gauge fields, leading to simple second order partial differential equations of motion, whose Newtonian and strong limits coincide to those o
f the Einsten-Hilbert action but the physics of its very weak fields should be identified through observation. We show that GVT is at least as dynamically stable as the Einstein-Hilbert gravity. It accommodates the MOND paradigm. We study its gravitational light deflection. We show that the post Newtonian parameter of $gamma$ vanishes in the MOND regime of GVT gravity. Since $Lambda$CDM assumes that $gamma=1$, this suggests to observationally measure the $gamma$ parameter in the weak regime of gravity as either a test for $Lambda$CDM or GVT models
We present a phenomenological model for the nature in the Finsler and Randers space-time geometries. We show that the parity-odd light speed anisotropy perpendicular to the gravitational equipotential surfaces encodes the deviation from the Riemann g
eometry toward the Randers geometry. We utilize an asymmetrical ring resonator and propose a setup in order to directly measure this deviation. We address the constraints that the current technology will impose on the deviation should the anisotropy be measured on the Earth surface and the orbits of artificial satellites.
We consider the AQUAL theory - a theory of modified gravity capable of resolving the missing mass problem - and study its predictions for micro gravity tests at the gravitational saddle points of the Solar system. We report that the AQUAL model enhan
ces the gravity at the sub-micrometer ranges around the gravitational saddle points in a way that so far has been unnoticed. This enhancement can be measured. We, therefore, call for moving toward implementing micrometer gravity tests within the Solar gravitational saddle points.
The MOND paradigm to the missing mass problem requires introducing a functional that is to be identified through observations and experiments. We consider AQUAL theory as a realization of the MOND. We show that the accurate value of the Earth GM meas
ured by the Lunar Laser Ranging and that by various artificial Earth satellites, including the accurate tracking of the LAGEOS satellites, constrain this functional such that some of the chosen/proposed functional are refuted.
We study the gravitomagnetism in the TeVeS theory. We compute the gravitomagnetic field that a slow-moving mass distribution produces in its Newtonian regime. We report that the consistency between the TeVeS gravitomagnetic field and that predicted b
y the Einstein-Hilbert theory leads to a relation between the vector and scalar coupling constants of the theory. We observe that requiring consistency between the near horizon geometry of a black hole in TeVeS and the image of the black hole taken Event Horizon Telescope leads to another relation between the coupling constants of the TeVeS theory and enable us to identify the coupling constants of the theory.
We report that a triangular Fabry-Perot resonator filled with a parity-odd linear anisotropic medium exhibiting the one-way light speed anisotropy acts as a perfect diode. A Linear crystal such as the nematic liquid crystals whose molecular structure
s break parity can exhibit the one-way light speed anisotropy. The one-way light speed anisotropy also can be induced in a non-linear medium in the presence of constant electric and magnetic field strengths.
