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Massive gravity may be viewed as a suitable limit of bimetric gravity. The limiting procedure can lead to an interesting interplay between the "background" and "foreground" metrics in a cosmological context. The fact that in bimetric…
Cosmological implications of a class of hybrid metric-Palatini gravity with a non-minimal matter-geometry coupling is considered. The theory contains a metric curvature tensor, together with a curvature tensor constructed from an…
Relevant deformations of gravity present an exciting window of opportunity to probe the rigidity of gravity on cosmological scales. For a single-graviton theory, the leading relevant deformation constitutes a graviton mass term. In this…
We study perturbations around some cosmological backgrounds in the dRGT theory of massive gravity. We develop a general formalism to calculate the perturbations around any background. We derive the Lagrangian for fluctuations in the small…
In this essay we propose that the theory of gravity's vacuum is described by a de Sitter geometry. Under this assumption we consider an adjustment mechanism able to screen any value of the vacuum energy of the matter fields. We discuss the…
Some models of modified gravity and their observational manifestations are considered. It is shown, that gravitating systems with mass density rising with time evolve to a singular state with infinite curvature scalar. The universe…
I present a model of discrete gravity, which is formulated in terms of a topological gauge theory with defects. The theory has no local degrees of freedom and the gravitational field is trivial everywhere except at a number of colliding…
A model in which the massive dilaton is introduced by minimally extending the two dimensional topological gravity is studied semi-classically. The theory is no longer topological because of the explicit Weyl scale symmetry breaking. Due to…
Taking a quantum corrected form of Raychaudhuri equation in a geometric background described by a Lorentz-violating massive theory of gravity, we go through investigating a time-like congruence of massive gravitons affected by a Bohmian…
In this short note we perform the Hamiltonian analysis of bimetric gravity with one particular form of potential between two metrics. We find that this theory have eight secondary constraints. We identify four constraints that are the first…
We consider spatially covariant modified gravity in which the would-be scalar degree of freedom is made non-dynamical and hence there are just two tensorial degrees of freedom, i.e., the same number of dynamical degrees of freedom as in…
We describe gauge theories which allow to retrieve a large class of gravitational theories, including, MacDowell-Mansouri gravity and its topological extension to Loop Quantum Gravity via the Pontrjagin characteristic class involving the…
Observational manifestations of some models of modified gravity, which have been suggested to explain the accelerated cosmological expansion, are analyzed for gravitating systems with time dependent mass density. It is shown that if the…
Quantum theory of the gravitation in the causal approach is studied up to the second order of perturbation theory. We prove gauge invariance and renormalizability in the second order of perturbation theory for the pure gravity system…
Modifications to gravity can provide attractive alternatives to the dark components of the standard model of cosmology. These modifications to general relativity (GR) must be hidden at small scales where theory is well tested, and so one…
The interaction of matter with gravity in two dimensional spacetimes can be supplemented with a geometrical force analogous to a Lorentz force produced on a surface by a constant perpendicular magnetic field. In the special case of constant…
The two-phase structure is imposed on the world continuum, with the graviton emerging as the tensor Goldstone boson during the spontaneous transition from the affinely connected phase to the metric one. The physics principle of…
We search for viable f(R) theories of gravity, making use of the equivalence between such theories and scalar-tensor gravity. We find that models can be made consistent with solar system constraints either by giving the scalar a high mass…
We consider general curvature-invariant modifications of the Einstein-Hilbert action that become important only in regions of extremely low space-time curvature. We investigate the far future evolution of the universe in such models,…
It is found that conformally coupled induced gravity with gradient torsion gives a dilaton gravity in Riemann geometry. In the Einstein frame of the dilaton gravity the conformal symmetry is hidden and a non-vanishing cosmological constant…