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The Weyl$-$Yang gravitational gauge theory is investigated in the structure of a pure higher-dimensional non-Abelian Kaluza$-$Klein background. We construct the dimensionally reduced field equations and stress-energy-momentum tensors as…
A standard model is formulated in a Weyl space, $W_4$, yielding a Weyl covariant dynamics of massless chiral Dirac fermion fields for leptons and quarks as well as the gauge fields involved for the groups D(1)\,(Weyl), $U(1)_Y{\times}…
The Weyl-Wigner-Moyal formalism for quantum particle with discrete internal degrees of freedom is developed. A one to one correspondence between operators in the Hilbert space $L^{2}(\mathbb{R}^{3})\otimes{\mathcal{H}}^{(s+1)}$ and…
Some of the simplest modifications to general relativity involve the coupling of additional scalar fields to the scalar curvature. By making a Weyl rescaling of the metric, these theories can be mapped to Einstein gravity with the…
The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these systems outside the critical…
We consider a Weyl invariant extension of Dirac-Born-Infeld type gravity. An appropriate choice of the metric hides the scalar degree of freedom which is required by the local scale invariance of the action at the first sight, and then a…
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…
Eventual flattening of velocity dispersion profiles of some galactic globular clusters in the Milky Way cannot be explained in the framework of Newtonian gravity and hence in general theory of relativity in the weak field limit, without…
Quintessence models have been widely examined in the context of scalar-Gauss-Bonnet gravity, a subclass of Horndeski's theory, and were proposed as viable candidates for Dark Energy. However, the relatively recent observational constraints…
Results on the isolation of the radiative degrees of freedom of the gravitational field with a positive cosmological constant in full General Relativity are put forward. Methods employed in a recent geometric characterisation of…
We use the Newtonian limit of a general scalar-tensor theory around a background field to study astrophysical effects. The gravitational theory modifies the standard Newtonian potential by adding a Yukawa term to it, which is quantified by…
We consider higher dimensional gravity in which the four dimensional spacetime and extra dimensions are not treated on an equal footing. The anisotropy is implemented in the ADM decomposition of higher dimensional metric by requiring the…
In this paper we obtain some cosmological solutions that describe the present period of accelerating expansion of the universe in the framework of a geometrical gauge scalar-tensor theory of gravity. The background geometry in the model is…
The Jackiw-Teitelboim gravity with the matter degrees of freedom is considered. The classical model is exactly solvable and its solutions describe non-trivial gravitational scattering of matter wave-packets. For huge amount of the solutions…
A model for quantized gravity coupled to matter in the form of a single scalar field is investigated in four dimensions. For the metric degrees of freedom we employ Regge's simplicial discretization, with the scalar fields defined at the…
Mathematical method of quantum phase space is very useful in physical applications like quantum optics and non-relativistic quantum mechanics. However, attempts to generalize it for the relativistic case lead to some difficulties. One of…
We employ the extended 1+3 orthonormal frame formalism for fluid spacetime geometries $({\cal M}, {\bf g}, {\bf u})$, which contains the Bianchi field equations for the Weyl curvature, to derive a 44-D evolution system of first-order…
We examine the possibility that the gravitational contribution to the entropy of a system can be identified with some measure of the Weyl curvature. In this paper we consider homothetically self-similar spacetimes. These are believed to…
The irreducible decomposition technique is applied to the study of classical models of metric-affine gravity (MAG). The dynamics of the gravitational field is described by a 12-parameter Lagrangian encompassing a Hilbert-Einstein term,…
We consider the problem of parametrizing modified gravity theories that include an additional vector field in the sub-Hubble regime within the quasi-static approximation. We start from the most general set of second order equations for…