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(Abridged Abstract) This paper deals with a number of technical achievements that are instrumental for a dis-solution of the so-called {\it Hole Argument} in general relativity. The work is carried through in metric gravity for the class of…
We study a noncommutative deformation of general relativity where the gravitational field is described by a matrix-valued symmetric two-tensor field. The equations of motion are derived in the framework of this new theory by varying a…
We present a metric theory of gravity with Lagrangian L = (8\pi G)^{-1}(\Xi g^{ii} - \Upsilon g^{00})\sqrt{-g} + L_{GR} + L_{matter} motivated by classical equations \partial_t \rho + \partial_i (\rho v^i) = 0 \partial_t (\rho v^j) +…
Causal rigid particles whose action includes an {\it arbitrary} dependence on the world-line extrinsic curvature are considered. General classes of solutions are constructed, including {\it causal tachyonic} ones. The Hamiltonian…
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…
In this work, we analyze the possibility of gravitationally induced matter creation in the so-called Energy-Momentum-Squared gravity (EMSG), i.e. $f(R,T_{\mu\nu}T^{\mu\nu})$ gravity, in its dynamically equivalent scalar-tensor…
The formulation of a dynamical theory of General Relativity, including matter, is viewed as a problem of coupling Einstein's theory of pure gravity, formulated as an action principle, to an independently chosen and well defined field theory…
We consider the G\"odel universe within the context of the local limit of nonlocal gravity. This theory differs from Einstein's general relativity (GR) through the existence of a scalar susceptibility function $S(x)$ that is a…
We discuss the galaxy clustering based on thermodynamics and statistical mechanics in the expanding universe in a modified theory of gravity. The modified general relativity (MGR) is developed using the regular line element field to…
The search for the physical mechanism underlying the observational evidence for the acceleration of the recent universe is a compelling goal of modern fundamental cosmology. Here we quantitatively study a class of homogeneous and isotropic…
We address the problem of the energy conditions in modified gravity taking into account the additional degrees of freedom related to scalar fields and curvature invariants. The latter are usually interpreted as generalized {\it geometrical…
The fundamental physical object of the Global Time Theory is a three-dimensional curved space dynamically developing in global time. The equations of its dynamics are derived from the Lagrangian, and the Hamiltonian of ravitation turns out…
The gravitino problem is investigated in the framework of Extended Gravity cosmologies. In particular, we consider $f(R)$ gravity, the most natural extension of the Hilbert-Einstein action, and $f(\cal T)$ gravity, the extension of…
It is widely accepted that the fundamental geometrical law of nature should follow from an action principle. The particular subset of transformations of a system's dynamical variables that maintain the form of the action principle comprises…
In this paper the causality issues are discussed in a non-Riemannian geometry, called Lyra geometry. It is a non-Riemannian geometry originated from Weyl geometry. In order to compare this geometry with the Riemannian geometry, the Einstein…
A non-topological Lorentz gauge model of gravity with torsion based on Gauss-Bonnet type Lagrangian is considered. The Lagrangian differs from the Lovelock term in four-dimensional space-time and has a number of interesting features. We…
We present a fully covariant and gauge-invariant analysis of linear cosmological perturbations in Energy-Momentum Squared Gravity. Working within the 1+3 formalism, we derive the exact propagation equations for scalar, vector, and tensor…
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,…
Classifying consistent effective field theories for the gravitational interaction has recently been the subject of intense research. Demanding the absence of causality violation in high energy graviton scattering processes has led to a…
We derive the equation of matter density perturbations on sub-horizon scales for a general Lagrangian density f(R, phi, X) that is a function of a Ricci scalar R, a scalar field phi and a kinetic term X=-(nabla phi)^2/2. This is useful to…