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A modified theory of gravity with the function $F(R) = R\exp(\alpha R)$ instead of Ricci scalar $R$ in the Einstein$-$Hilbert action is considered and analyzed. The action of the model is converted into Einstein$-$Hilbert action at small…
Recently a new approach in constructing the conserved charges in cosmological Einstein's gravity was given. In this new formulation, instead of using the explicit form of the field equations a covariantly conserved rank four tensor was…
Using as inspiration the well known chiral effective lagrangian describing the interactions of pions at low energies, in these lectures we review the quantization procedure of Einstein gravity in the spirit of effective field theories. As…
The topological aspects of Einstein gravity suggest that topological invariance could be a more profound principle in understanding quantum gravity. In this work, we explore a topological supergravity action that initially describes a…
A deformation of Einstein Gravity is constructed based on gauging the noncommutative ISO(3,1) group using the Seiberg-Witten map. The transformation of the star product under diffeomorphism is given, and the action is determined to second…
A multidimensional gravitational model on the manifold $M = M_0 \times \prod_{i=1}^{n} M_i$, where M_i are Einstein spaces ($i \geq 1$), is studied. For $N_0 = dim M_0 > 2$ the $\sigma$ model representation is considered and it is shown…
It is shown that if a metric in quantum gravity can be decomposed as a sum of classical and quantum parts then Einstein quantum gravity looks approximately like modified gravity with a nonminimal interaction between gravity and matter.
In this paper, we construct and study solutions of Einstein's equations in vacuum with a positive cosmological constant which can be considered as inhomogeneous generalizations of the Nariai cosmological model. Similar to this Nariai…
The disformal transformation of metric $g_{\mu \nu} \to \Omega^2 (\phi)g_{\mu \nu}+\Gamma(\phi,X) \partial_{\mu}\phi \partial_{\nu}\phi$, where $\phi$ is a scalar field with the kinetic energy $X= \partial_{\mu}\phi \partial^{\mu}\phi/2$,…
Consistency of Einstein's gravitational field equation $G_{\mu\nu} \propto T_{\mu\nu}$ imposes a "conservation condition" on the $T$-tensor that is satisfied by (i) matter stress tensors, as a consequence of the matter equations of motion,…
Dark energy cosmology is considered in a modified Gauss-Bonnet model of gravity with and without a scalar field. It is shown that these generalizations of General Relativity endow it with a very rich cosmological structure: it may naturally…
We consider a maximal extension of the Hilbert-Einstein action and analyze several interesting features of the theory. More specifically, the motion is non-geodesic and takes place in the presence of an extra force. These models could lead…
We construct a class of Einstein-vector theories where the vector field couples bilinearly to the curvature polynomials of arbitrary order in such a way that only Riemann tensor rather than its derivative enters the equations of motion. The…
We study Finsler black holes induced from Einstein gravity as possible effects of quantum spacetime noncommutativity. Such Finsler models are defined by nonholonomic frames not on tangent bundles but on (pseudo) Riemannian manifolds being…
This thesis focuses on modifications on Einstein's theory of General Relativity, which could explain the current problems in gravitation and cosmology. More specifically, modifications of the affine structure of the spacetime, which is the…
The starting point of this work is the original Einstein action, sometimes called the Gamma squared action. Continuing from our previous results, we study various modified theories of gravity following the Palatini approach. The metric and…
We investigate the metric perturbations of the restricted f(R) theory of gravity in the cosmological context and explore the phenomenological implications of this model. We show that it is possible to construct a restricted model of…
Modified Einstein's equations implementing both an energy-dependent Newtonian and cosmological constant can be obtained via a modified action characterised by a non-minimal gravity-matter coupling. We show how different dynamics for the…
We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modifcation introduced in the cosmological equations leads to several new…
An integral kernel representation for the commutative $\star$-product on curved classical spacetime is introduced. Its convergence conditions and relationship to a Drin'feld differential twist are established. A $\star$-Einstein field…