The quantities ml and ms are the masses of two objects whose spatial separation is R. The value of the constant of proportionality, G, was not known to Newton and, in fact, was not accurately determined until the latter half of the nineteenth century. The calculation of its value was based on the results of an experiment to determine the density of the earth performed by Henry Cavendish, and pu...

We have derived the invariants of cosmological models with Gurzadyan-Xue dark energy, along with the solutions for any time dependent light speed and gravitational constant. The correspondence of the invari-ants with the separatrices found earlier for the GX-models in [4] is shown, and hence the basis of then detected hidden symmetry is now revealed. Solutions are derived both for radiation and...

A fully relativistic modified gravitational theory including a fifth force skew symmetric field is fitted to the Pioneer 10/11 anomalous acceleration. The theory allows for a variation with distance scales of the gravitational constant G, the fifth force skew symmetric field coupling strength ω and the mass of the skew symmetric field μ = 1/λ. A fit to the available anomalous acceleration data ...

We construct the covariant nonlocal action for recently suggested long-distance modifications of gravity theory motivated by the cos-mological constant and cosmological acceleration problems. This construction is based on the special nonlocal form of the Einstein-Hilbert action explicitly revealing the fact that this action within the covariant curvature expansion begins with curvature-squared ...

If the gravitational interaction is unified with the electro-weak and strong interactions at a mass M = 10 15 GeV, the evolution of Newton's constant must differ from its classical (general relativistic) form. We can model such behavior by introducing an ad hoc dependence on ℓn(s/4m 2), where s is the usual cm energy between two protons. We can then predict the observable effects for relativist...