Abstract
In theories where a scalar field couples nonminimally to gravity, the effective gravitational “constant” becomes dependent on the value of the scalar field. This note first gives a brief review on how the cosmological evolution provides a dynamical stabilization for the gravitational “constant” as the system relaxes towards general relativity in matter dominated and potential dominated regimes for scalar-(curvature)tensor and scalar-torsion gravities. Second part summarizes the radius dependence of the gravitational “constant” around a point mass in the parametrized post-Newtonian formalism for scalar-tensor and multiscalar-tensor gravity.
Highlights
General relativity (GR) which ascribes the effects of gravity to the curvature of spacetime has been highly successful in describing a wide range of phenomena
Are consistent with no significant distance variation of the gravitational constant or a Yukawa type correction. In principle these observations can be employed to constrain the parameters of the models with nonminimally coupled scalar fields, that task remains beyond the scope of the present note
We considered the extensions of general relativity and teleparallel equivalent of general relativity by nonminimally coupled scalars to curvature or torsion, respectively
Summary
General relativity (GR) which ascribes the effects of gravity to the curvature of spacetime has been highly successful in describing a wide range of phenomena. The current account of the evolution and structures of the universe entails attributing roughly 25% of the overall energy density to a host of invisible unknown particles as dark matter, while further 70% is taken by the cosmological constant which is way too small to receive a natural explanation as a vaccuum energy density of fundamental fields This puzzle has motivated an intensive research effort in studying various extensions of general relativity that would leave the small scale and weak gravity regimes intact, but suitably modify the large scale physics with some effects permitted in the strong gravity regime [1,2,3].
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