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Using dimensional analysis techniques we present an extension of Newton's gravitational theory built under the assumption that Milgrom's acceleration constant is a fundamental quantity of nature. The gravitational force converges to…
We generalize tensor-scalar theories of gravitation by the introduction of an abnormally weighting type of energy. This theory of tensor-scalar anomalous gravity is based on a relaxation of the weak equivalence principle that is now…
The observed excess of gravitational forces in galaxies and galactic clusters is usually referred as the existence of "dark matter particles" of unknown origin. An alternative explanation of the dark matter effect is presented here by…
Questioning the experimental basis of continuous descriptions of fundamental interactions we discuss classical gravity as an effective continuous first-order approximation of a discrete interaction. The sub-dominant contributions produce a…
It is shown that the cosmological constant links the roots both of General Relativity and Newtonian gravity via the general function satisfying Newton's theorem according to which the gravitating sphere acts as a point mass situated in its…
The missing gravity in galaxies requires dark matter, or alternatively a modification of gravity or inertia. These theoretical possibilities of fundamental importance may be distinguished by the statistical relation between the observed…
Modified Newtonian dynamics (MOND) is an empirically motivated modification of Newtonian gravity or inertia suggested by Milgrom as an alternative to cosmic dark matter. The basic idea is that at accelerations below a0 ~ 10^{-8} cm/s^2 ~…
Towards the goal to quantize gravity, in this short review we discuss an intermediate step which consists in extending the picture of standard General Relativity by considering Extended Theories of Gravity. In this tapestry, the equations…
The observed matter in the universe accounts for just 5 percent of the observed gravity. A possible explanation is that Newton's and Einstein's theories of gravity fail where gravity is either weak or enhanced. The modified theory of…
We present a concise description of the basic features of gravity-matter models based on the formalism of non-canonical spacetime volume-forms in its two versions: the method of non-Riemannian volume-forms (metric-independent covariant…
The linearized Einstein theory in the approximately flat time-space is modified accounting for a massive graviton as a dark matter in the universe. On the basis of magnetic-type Maxwell- Proca -Vlasov equations, the interactions of the…
Modified gravity theories with a nonminimal coupling between curvature and matter offer a compelling alternative to dark energy and dark matter by introducing an explicit interaction between matter and curvature invariants. Two of the main…
In this study one resorts to the phenomenology of models endowed with a non-minimal coupling between matter and geometry, in order to develop a mechanism through which dynamics similar to that due to the presence of dark matter is…
In the context of the fact that the existence of dark energy causing the accelerated expansion of the universe has been confirmed by the WMAP and the Sloan Digital Sky Survey, we re-examine gravitation itself, starting with the formulation…
We consider the possibility of an alternative gravity theory explaining the dynamics of galactic systems without dark matter. From very general assumptions about the structure of a relativistic gravity theory we derive a general expression…
Scalar-tensor theories of gravity that embrace conformal coupling to the scalar curvature are the focal point of cosmology on discussions of inflation and late-time accelerating universe. Although there exists a stringent nucleo-synthesis…
I examine how two specific examples of modified gravity explanations of cosmic acceleration help us understand some general problems confronting cosmological tests of gravity: how do we distinguish modified gravity from dark energy if they…
All observational evidence for dark matter and dark energy is so far exclusively gravitational. Hence, the dark sector may be equivalently described by a theory of the spacetime metric whose dynamics is affected by interactions with an…
Massive gravity with second and fourth derivatives is shown to give both attractive and repulsive gravities. In contrast to the attractive gravity correlated with the energy-momentum tensor, the repulsive gravity is related to a fixed mass…
We analyze the behavior of the scalar field as dark energy of the Universe in a static world of galaxies and clusters of galaxies. We find the analytical solutions of evolution equations of the density and velocity perturbations of dark…