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We formulate an approach to the geometry of Riemann-Cartan spaces provided with nonholonomic distributions defined by generic off-diagonal and nonsymmetric metrics inducing effective nonlinear and affine connections. Such geometries can be…
Certain 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. We prove this statement by constructing exact and approximate…
The no-boundary proposal is a theory of the initial conditions of the universe formulated in semi-classical gravity, and relying on the existence of regular (complex) solutions of the equations of motion. We show by explicit computation…
In this short review, we discuss the approach of the commutator algebra of covariant derivative to analyse the gravitational theories, starting from the standard Einstein's general theory of relativity and focusing on the Rastall theory.…
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…
In this report, we discuss a candidate mechanism through which one might address the various cosmological constant problems. We first observe that the renormalization of gravitational couplings (induced by integrating out various matter…
The possibility of testing spatial noncommutativity by current experiments on normal quantum scales is investigated. For the case of both position-position and momentum-momentum noncommuting spectra of ions in crossed electric and magnetic…
Deformation quantization is a powerful tool to quantize some classical systems especially in noncommutative space. In this work we first show that for a class of special Hamiltonian one can easily find relevant time evolution functions and…
Using the Cartan formulation of General Relativity, we construct a well defined lattice-regularized theory capable to describe large non-perturbative quantum fluctuations of the frame field (or the metric) and of the spin connection. To…
A modification of General Relativity that is based on the gravitational Standard-Model Extension and incorporates nondynamical background fields has recently been studied via the ADM formalism. Our objective in this paper is to develop a…
Noncommutative oscillators are first-quantized through an abelian Drinfel'd twist deformation of a Hopf algebra and its action on a module. Several important and subtle issues making possible the quantization are solved. The spectrum of the…
We investigate the cosmological applications of a bi-scalar modified gravity that exhibits partial conformal invariance, which could become full conformal invariance in the absence of the usual Einstein-Hilbert term and introducing…
Quantum power corrections to the gravitational spin-orbit and spin-spin interactions, as well as to the Lense-Thirring effect, were found for particles of spin 1/2. These corrections arise from diagrams of second order in Newton…
General Relativity with nonvanishing torsion has been investigated in the first order formalism of Poincare gauge field theory. In the presence of torsion, either side of the Einstein equation has the nonvanishing covariant divergence. This…
We outline how Drinfeld twist deformation techniques can be applied to the deformation quantization of principal bundles into noncommutative principal bundles, and more in general to the deformation of Hopf-Galois extensions. First we twist…
It is well known that the Einstein-Hilbert action in two dimensions is topological and yields an identically vanishing Einstein tensor. Consequently one is faced with difficulties when formulating a non-trivial gravity model. We present a…
We compute the first nontrivial noncommutative correction to the Einstein-Hilbert Lagrangian, which arises from the double copy of noncommutative Yang-Mills theory (ncYM). We start by considering linear and quadratic $\theta$-corrections up…
We discuss the role of gravitational corrections to the running of the electric charge through the evaluation of scattering amplitudes of charged particles in massless scalar electrodynamics. Computing the complete divergent part of the…
The linearized Einstein field equations with the renormalized stress tensor of a massless quantum scalar field as source are solved in the 4-dimensional spacetime near an infinite plane boundary. The motion of particles and light is…
We consider conformally invariant form of the actions in Einstein, Weyl, Einstein-Cartan and Einstein-Cartan-Weyl space in general dimensions($>2$) and investigate the relations among them. In Weyl space, the observational consistency…