Related papers: Five-dimensional generalized $f(R)$ gravity with c…
The vector nature of magnetic fields and the geometrical interpretation of gravity introduced by general relativity, guarantee a special coupling between magnetism and spacetime curvature. This magneto-geometrical interaction effectively…
We extend the usual vacuum Metric-Affine $f(R)$ Gravity by supplementing it with all parity even quadratic invariants in torsion and non-metricity. As we show explicitly this supplementation drastically changes the status of the Theory…
We propose the mimetic $F(R)$ theory and investigate the early-time and late-time acceleration in such theory. It is demonstrated that inflation consistent with observable data may be realized in such theory. The reconstruction of realistic…
We propose in this paper a mathematicians' view of the Kaluza-Klein idea of a five dimensional space-time unifying gravitation and electromagnetism, and extension to higher-dimensional space-time. By considering the classification of…
The curvature of a spacetime, either in a topological sense, or averaged over super-horizon-sized patches, is often equated with the global curvature term that appears in Friedmann's equation. In general, however, the Universe is…
We review some recent developments in the conformal gravity theory that has been advanced as a candidate alternative to standard Einstein gravity. As a quantum theory the conformal theory is both renormalizable and unitary, with unitarity…
Recently, in a series of papers, we established the existence and found a general solution for the simultaneously rotating and twisting locally rotationally symmetric spacetimes in general relativity, which can model inhomogeneous and…
We investigate the existence of black bounce solutions in $2+1$ dimensions within the framework of $f(R)$ gravity. We analyze whether black bounce geometries originally obtained in general relativity can be consistently generalized to…
The recent interest in modified theories of gravity, involving some type of non-minimal coupling to the Ricci scalar, and the calculation of cosmological observables in the Einstein or the Jordan frame, motivate the formulation of these…
Corrections to Newton's inverse law have been so far considered, but not clear in warped higher dimensional worlds, because of complexity of the Einstein equation. Here we give a model of a warped 6D world with an extra 2D sphere. We take a…
We derive curvature counterterms in two-dimensional gravity coupled to conformal matter up to infinite order. By construction the higher-order action is equivalent to a finite first-order theory with auxiliary scalar. Due to this…
In braneworld models, Space-Time-Matter and other Kaluza-Klein theories, our spacetime is devised as a four-dimensional hypersurface {\it orthogonal} to the extra dimension in a five-dimensional bulk. We show that the FRW line element can…
This work presents the foundations of Singular Semi-Riemannian Geometry and Singular General Relativity, based on the author's research. An extension of differential geometry and of Einstein's equation to singularities is reported.…
Various Hamiltonian formulations of f(R) gravity can be found in the literature. Some authors follow the Ostrogradsky treatment of higher derivative theories and introduce as extra variables first order time derivatives of the metric…
We survey the landscape of $f(R)$ theories of gravity in their various formulations, which have been used to model the cosmic acceleration as alternatives to dark energy and dark matter. Besides, we take into account the problem of…
Off-diagonal vacuum and nonvacuum configurations in Einstein gravity can mimic physical effects of modified gravitational theories of $f(R,T,R_{\mu \nu}T^{\mu \nu})$ type. To prove this statement, exact and approximate solutions are…
A modified theory of general relativity is proposed, where the gravitational constant is replaced by a dynamical variable in space-time. The dynamics of the gravitational coupling is described by a family of parametrized null geodesics,…
New corrections to General Relativity are considered in the context of modified $f(R)$ gravity, that satisfy cosmological and local gravity constraints. The proposed models behave asymptotically as $R-2\Lambda$ at large curvature and show…
The paper deals with $f(R)$ gravity theory in the background of inhomogeneous FLRW--type space time model. With proper choice of the inhomogeneous metric function it is possible to have an emergent scenario for the $f(R)$--cosmology.…
In the previous paper we examined the third quantization of the $f(R)$-type gravity and studied the Heisenberg uncertainty relation of the universe in the example of $f(R)=R^2$. In this work the Heisenberg uncertainty relation of the…