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In earlier work it was shown that a weak modification of general relativity, in the linearized approach, renders a spherically symmetric and stationary model of the Universe. This was due to the presence of a third mode of polarization in…
I review the problem of dark energy focusing on the cosmological constant as the candidate and discuss its implications for the nature of gravity. Part 1 briefly overviews the currently popular `concordance cosmology' and summarises the…
We review various modified gravities considered as gravitational alternative for dark energy. Specifically, we consider the versions of $f(R)$, $f(G)$ or $f(R,G)$ gravity, model with non-linear gravitational coupling or string-inspired…
The analysis of measurements of accelerated observers in Minkowski spacetime has led to the development of nonlocal special relativity theory. Inertia and gravitation are intimately connected in accordance with the principle of equivalence.…
Relying on a fundamental empirical identity of heavy and inertial mass it is proposed to bring a status of general theory of relativity (GTR) of Einstein up to a level of Unified Field Theory. To do this, a thoroughgoing revision of…
This a brief review on $F(T)$ gravity and its relation with k-essence. Modified teleparallel gravity theory with the torsion scalar has recently gained a lot of attention as a possible explanation of dark energy. We perform a thorough…
In the non-relativistic theory of gravitation recently proposed by Horava, the Hamiltonian constraint is not a local equation satisfied at each spatial point but an equation integrated over a whole space. The global Hamiltonian constraint…
We study capability of $f(R)$ gravity models to allow crossing the phantom boundary in both Jordan and Einstein conformal frames. In Einstein frame, these models are equivalent to Einstein gravity together with a scalar field minimally…
Recent work has shown that non-local modifications of gravity involving terms such as $m^2R\Box^{-2}R$ (and no cosmological constant) provide a phenomenologically viable alternative to $\Lambda$CDM. We first discuss the possibility that…
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…
To the astrophysicist faced with the puzzle of dark matter, this one appears under two different aspects: on the one hand in cosmology, i.e. at very large scales, where it seems to be made of a bath of particles; on the other hand at the…
In this thesis we will focus on Einstein's interpretation of gravity. We will examine how the most famous equations in cosmology are derived from GR and also some results of cosmological significance. We will see how combining that with…
The back-reaction of a classical gravitational field interacting with quantum matter fields is described by the semiclassical Einstein equation, which has the expectation value of the quantum matter fields stress tensor as a source. The…
A new term describing interactions between charge and potentials may be added to the right hand side of the Einstein equations. In the proposed term an additional tensor has been introduced containing a charge density, analogous to the…
We investigate realistic models of compact objects, focusing on neutron and strange stars, composed by dense matter and dark energy in the form of a simple fluid or scalar field interacting with matter. For the dark energy component, we use…
In contrast to the phenomenon of nullification of the cosmological constant in the equilibrium vacuum, which is the general property of any quantum vacuum, there are many options in modifying the Einstein equation to allow the cosmological…
We investigate the cosmological implications of modified gravities induced by the quantum fluctuations of the gravitational metric. If the metric can be decomposed as the sum of the classical and of a fluctuating part, of quantum origin,…
In this letter, we consider the possibility of reconciling metric theories of gravitation with violation of the conservation of energy-momentum. Under some circumstances, this can be achieved in the context of unimodular gravity, and it…
In this paper, we will analyse the cosmological models in Einstein-aether gravity, which is a modified theory of gravity in which a time-like vector field breaks the Lorentz symmetry. We will use this formalism to analyse different…
The recent starting of the gravitational wave (GW) astronomy with the events GW150914, GW151226, GW170104, and the very recent GW170814 and GW170817 seems to be fundamental not only in order to obtain new intriguing astrophysical…