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Detailed knowledge of the different classes of stellar orbits that can be accommodated in a given galactic potential is a prerequisite when building self-consistent models using for instance the Schwazschild technique. Furthermore,…
The discovery of the accelerated expansion of the Universe has had a vast resonance on a number of physical disciplines. In recent years several viable modified gravity models have been proposed, which naturally lead to a late-time de…
In our current cosmological model, the main constituents of the Universe are dark matter and dark energy, whose nature is unknown, and for which there is no place in the standard model of particle physics. How to include dark matter and…
Over the past decades, General Relativity and the concordance $\Lambda$CDM model have been successfully tested using several different astrophysical and cosmological probes based on large datasets ({\it precision cosmology}). Despite their…
In the current framework of Einstein's equations in general relativity (GR), gravity is described by the spacetime curvature. However, there are other descriptions where the origin of gravity can be understood through torsion and…
The evidence of the acceleration of universe at present time has lead to investigate modified theories of gravity and alternative theories of gravity, which are able to explain acceleration from a theoretical viewpoint without the need of…
The universe is viewed as a dust gas filling a sphere and floating in infinite empty space. Einstein's gravitational equations are applied to this case together with appropriate boundary values. The equations are solved for initial…
The Friedmann equation is derived for a Newtonian universe. Changing mass density to energy density gives exactly the Friedmann equation of general relativity. Accounting for work done by pressure then yields the two Einstein equations that…
Milgrom's modified Newtonian dynamics (MOND) has done a great job on accounting for the rotation curves of a variety of galaxies by assuming that Newtonian dynamics breaks down for extremely low acceleration typically found in the galactic…
Torsion and curvature could play a fundamental role in explaining cosmological dynamics. f(R)-gravity with torsion is an approach aimed to encompass in a comprehensive scheme all the Dark Side of the Universe (Dark Energy and Dark Matter).…
A general account of MOND theory is given. I start with the basic tenets of MOND, which posit departure from standard dynamics in the limit of low acceleration -- below an acceleration constant a0 -- where dynamics become scale invariant. I…
Modified gravity theories have received increased attention lately to understand the late time acceleration of the universe. This viewpoint essentially modifies the geometric components of the universe. Among numerous extension to…
In this work we propose a new general model of eternal cyclic Universe. We start from the assumption that quantum gravity corrections can be effectively accounted by the addition of higher order curvature terms in the Lagrangian density for…
We examine an extension of General Relativity with an explicit non-minimal coupling between matter and curvature. The purpose of this work is to present an overview of the implications of the latter to various contexts, ranging from…
In this paper, we investigate the recently proposed relativistic theory for MOND using the phase space analysis. Unlike its precedent theory, namely TeVeS, this theory is claimed to agree with the observed Cosmic Microwave Background and…
In the framework of the special theory of relativity, the relativistic theory of gravitation (RTG) is constructed. The energy-momentum tensor density of all the matter fields (including gravitational one) is treated as a source of the…
The standard model of elementary particle physics and the theory of general relativity can be extended by the introduction of a vacuum variable which is responsible for the near vanishing of the present cosmological constant (vacuum energy…
The expansion of our universe, when followed backward in time, implies that it emerged from a phase of huge density, the big bang. These stages are so extreme that classical general relativity combined with matter theories is not able to…
We show that a number of problems of modern cosmology may be solved in the framework of multidimensional gravity with high-order curvature invariants, without invoking other fields. We use a method employing a slow-change approximation,…
Although it was proved that the Nash theory doesn't have classical Einstein limits, it has been proven to be formally divergent free and considered to be of interest in constructing theories of quantum gravity. The original Nash gravity…