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Despite its elegance, the theory of General Relativity is subject to experimental, observational, and theoretical scrutiny to arrive at tighter constraints or an alternative, more preferred theory. In alternative gravity theories, the…
Newton's gravitational constant $G$ has been measured to high accuracy in a number of independent experiments. For currently unresolved reasons, indicated values from different well-designed and thoroughly analyzed experiments differ by…
In a recent work, Dai (arXiv:2103.11157) searched for a variability in Newton's constant $G$ using the IGETS based gravitational acceleration measurements. However, this analysis, obtained from $\chi^2$ minimization, did not incorporate the…
The Newtonian approximation with a nonvanishing nonlocal background field is analyzed for the scalar-tensor nonlocal gravity and nonlocal Gauss-Bonnet gravity. For these two theories, our calculations show that the Newtonian gravitational…
The standard model for galaxy bias is built in a Newtonian framework, and several attempts have been made in the past to put it in a relativistic framework. The focus of past works was, however, to use the same Newtonian formulation, but to…
The discrepancies between recently reported experimental values of the gravitational constant were analysed within an inertia interpretation of MOND theory. According to this scenario the relative gravitational acceleration between a test…
In classical gravity deviations from the predictions of the Einstein theory are often discussed within the framework of the conformal Newtonian gauge, where scalar perturbations are described by two potentials $\phi$ and $\psi$. In this…
We consider the application of quantum corrections computed using renormalization group arguments in the astrophysical domain and show that, for the most natural interpretation of the renormalization group scale parameter, a gravitational…
The Generalized Uncertainty Principle (GUP) has been directly applied to the motion of (macroscopic) test bodies on a given space-time in order to compute corrections to the classical orbits predicted in Newtonian Mechanics or General…
We use a particular machine learning approach, called the genetic algorithms (GA), in order to place constraints on deviations from general relativity (GR) via a possible evolution of Newton's constant $\mu\equiv…
In this paper we directly constrain possible spatial variations of the Newtonian gravitational constant G over ranges 0.01-5 AU in various extrasolar multi-planet systems. By means of the third Kepler's law we determine the quantity \Gamma_…
We use IGETS absolute gravitational acceleration measurement data to study the gravitational acceleration variance. The relative variance of $\delta g /g$ in 22 years is less than $4\times 10^{-8}$. Since $\delta G /G\lessapprox\delta g /g…
We study the variation of the gravitational Newton's constant on cosmological scales in scalar-tensor theories of gravity. We focus on the simplest models of scalar-tensor theories with a coupling to the Ricci scalar of the form $F(\sigma)…
In the scalar tensor gravitational theories Newton's constant G_N evolves in the expanding universe. Likewise, it has been speculated that the acceleration scale a_0 in Milgrom's modified Newtonian dynamics (MOND) is tied to the scale of…
Although general relativity underlies modern cosmology, its applicability on cosmological length scales has yet to be stringently tested. Such a test has recently been proposed, using a quantity, EG, that combines measures of large-scale…
About 300 experiments have tried to determine the value of the Newtonian gravitational constant, G, so far, but large discrepancies in the results have made it impossible to know its value precisely. The weakness of the gravitational…
Theories of modified gravity generically violate the strong equivalence principle, so that the internal dynamics of a self-gravitating system in free fall depends on the strength of the external gravitational field (the external field…
The Newtonian constant of gravitation, $G$, stands out in the landscape of the most common fundamental constants owing to its surprisingly large relative uncertainty, which is attributable mostly to the dispersion of the values measured for…
As is well known, there exist some Lorentz breaking scenarios which explain the smallness of the cosmological constant in the present era. An important aspect to analyze is the propagation of gravitational waves and the screening or…
The location-scale model is usually present in physics and chemistry in connection to the Birge ratio method for the adjustment of fundamental physical constants such as the Planck constant or the Newtonian constant of gravitation, while…