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It is nowadays clear that General Relativity cannot be the definitive theory of Gravitation due to several shortcomings that come out both from theoretical and experimental viewpoints. At large scales (astrophysical and cosmological) the…

After reviewing the meaning of various equivalence principles and the structure of electrodynamics, we give a fairly detailed account of the construction of the light cone and a core metric from the equivalence principle for the photon (no…

Some problems of cosmology: the big bang singularity, the origin of conventional matter, of dark matter and of dark energy may be successfully described and treated in the framework of the Weyl-Dirac theory. This theory, being a minimal…

The absence of an identified consequence at solar system scale of the cosmological space expansion is usually explained considering that space expansion does not affect local anysotropies in matter distribution. This can also be explained…

We consider covariant metric theories of coupled gravity-matter systems satisfying the following two conditions: First, it is assumed that, by a hyperbolic reduction process, a system of first order symmetric hyperbolic partial differential…

The Friedmann equations of general relativity can be derived from the first law of thermodynamics when the entropy of the apparent horizon of a spatially isotropic universe is given by the Bekenstein-Hawking entropy. We point out that if…

This article is concerned with the derivation of the Gauss-Codazzi's constraints equations on the initial light cone for geometric transport equations in general relativity. Temporal-gauge-dependent constraints are addressed too and…

Einstein-aether theory is general relativity coupled to a dynamical unit timelike vector field. A brief review of current theoretical understanding and observational constraints on the four coupling parameters of the theory is given.

A new gauge theory of gravity is presented. The theory is constructed in a flat background spacetime and employs gauge fields to ensure that all relations between physical quantities are independent of the positions and orientations of the…

Aether theory is introduced to implement the violation of the Lorentz invariance in general relativity. For this purpose a unit timelike vector field introduced to theory in addition to the metric tensor. Aether theory contains four free…

Dark energy in General Relativity is typically non-interacting with other matter. However, it is possible that the dark energy interacts with the dark matter, and in this case, the dark matter can violate the universality of free fall (the…

Consistency relations involving the soft limit of the (n + 1)-correlator functions of dark matter and galaxy overdensities can be obtained, both in real and redshift space, thanks to the symmetries enjoyed by the Newtonian equations of…

Einstein-Cartan theory is an extension of the standard formulation of General Relativity characterized by a non-vanishing torsion. The latter is sourced by the matter fields via the spin tensor, and its effects are expected to be important…

According to this principle, the relativistic changes occurring to the bodies, after velocity changes, cannot be detected by observers moving with them because bodies and stationary radiations change in identical proportion after identical…

An analysis of composite inertial motion (relativistic sum) within the framework of special relativity leads to the conclusion that every translational motion must be the symmetrically composite relativistic sum of a finite number of quanta…

It was generally believed that, in general relativity, the fundamental laws of nature should be invariant or covariant under a general coordinate transformation. In general relativity, the equivalence principle tells us the existence of a…

Gravitation, according to General Relativity, is an attribute of space-time's geometry and hence not a force in the Newtonian sense. This is a consequence of Einstein's equivalence principle, which so far passed all experimental tests with…

A variational principle was recently suggested by Goenner, where an independent metric generates the spacetime connection. It is pointed out here that the resulting theory is equivalent to the usual Palatini theory. However, a bimetric…

The Einstein-Aether theory provides a simple, dynamical mechanism for breaking Lorentz invariance. It does so within a generally covariant context and may emerge from quantum effects in more fundamental theories. The theory leads to a…

The paper is devoted to fundamental problems of the Wheeler - DeWitt quantum geometrodynamics, which was the first attempt to apply quantum principles to the Universe as a whole. Our purpose is to find out the origin of these problems and…