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We review (and extend) the analysis of general theories of all interactions (gravity included) where the mass scales are due to dimensional transmutation. Quantum consistency requires the presence of terms in the action with four…
The concept of smooth deformations of a Riemannian manifolds, recently evidenced by the solution of the Poincar\'e conjecture, is applied to Einstein's gravitational theory and in particular to the standard FLRW cosmology. We present a…
I consider theories of gravity built not just from the metric and affine connection, but also other (possibly higher rank) symmetric tensor(s). The Lagrangian densities are scalars built from them, and the volume forms are related to…
The presence of a non-zero cosmological term in Einstein field equations can be interpreted as the physical possibility for preferred reference frames without breaking of general covariance. This possibility is used in the process of…
We show that a vector field non-minimally coupled to gravity reproduces exactly the dynamics of an Einstein cluster -- a large ensemble of non-interacting particles moving on circular geodesics under their collective gravitational field.…
In this article, we propose different background models of extended theories of gravity, which are minimally coupled to the SM fields, to explain the possibility of genesis of dark matter without affecting the SM particle sector. We modify…
We continue recent work and formulate the gravitational vacuum Einstein equations over a locally finite spacetime by using the basic axiomatics, techniques, ideas and working philosophy of Abstract Differential Geometry. The whole…
A modified Einstein-Gauss-Bonnet gravity in four dimensions where the quadratic Gauss-Bonnet term is coupled to a scalar field is considered. The field equations of the model are obtained by variational methods by making use of the…
We show how the Einstein equations with cosmological constant (and/or various types of matter field sources) can be integrated in a very general form following the anholonomic deformation method for constructing exact solutions in four and…
We summarize recent results on $D$-dimensional Robinson-Trautman solutions of Einstein's gravity in the presence of a conformally invariant non-linear electromagnetic field and a cosmological constant. These spacetimes contain static dyonic…
In this review we present a thoroughly comprehensive survey of recent work on modified theories of gravity and their cosmological consequences. Amongst other things, we cover General Relativity, Scalar-Tensor, Einstein-Aether, and Bimetric…
A geometric procedure is elaborated for transforming (pseudo) Riemanian metrics and connections into canonical geometric objects (metric and nonlinear and linear connections) for effective Lagrange, or Finsler, geometries which, in their…
We consider metric-affine scenarios where a modified gravitational action is sourced by electrovacuum fields in a three dimensional space-time. Such scenarios are supported by the physics of crystalline structures with microscopic defects…
A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for…
We analyze the stability of the Einstein static universe by considering homogeneous scalar perturbations in the context of f(R) modified theories of gravity. By considering specific forms of f(R), the stability regions of the solutions are…
We propose a phenomenological approach to the cosmological constant problem based on generally covariant non-local and acausal modifications of four-dimensional gravity at enormous distances. The effective Newton constant becomes very small…
We analyze the foundations of Finsler gravity theories with metric compatible connections constructed on nonholonomic tangent bundles, or (pseudo) Riemannian manifolds. There are considered "minimal" modifications of Einstein gravity…
We consider predictions for structure formation from modifications to general relativity in which the Einstein-Hilbert action is replaced by a general function of the Ricci scalar. We work without fixing a gauge, as well as in explicit…
We show that in the $f(Q)$ gravity with a non-metricity scalar $Q$, the curvatures in Einstein's gravity, that is, the Riemann curvature constructed from the standard Levi-Civita connection, could not be excluded or naturally appear. The…
Recent astrophysical data indicate that our universe might currently be in a de Sitter (dS) phase. The importance of dS space has been primarily ignited by the study of the inflationary model of the universe and the quantum gravity. As we…