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The equations of motion describing all physical systems, except gravity, remain invariant if a constant is added to the Lagrangian. In the conventional approach, gravitational theories break this symmetry exhibited by all other physical…
A non-geometrical (but with curved space) theory of gravitation characterized by a vector field representing gravitational matter and a metric tensor presenting space is presented. It is derived from a more general theory of matter and…
We exploit an interpretation of gravity as the symmetry broken phase of a de Sitter gauge theory to construct new solutions to the first order field equations. The new solutions are constructed by performing large $Spin(4,1)$ gauge…
We construct a model of quantum gravity in which dimension, topology and geometry of spacetime are dynamical. The microscopic degree of freedom is a real rectangular matrix whose rows label internal flavours, and columns label spatial…
Lattice spinor gravity is a proposal for regularized quantum gravity based on fermionic degrees of freedom. In our lattice model the local Lorentz symmetry is generalized to complex transformation parameters. The difference between space…
The so-called $\Gamma\Gamma$-form of the gravitational Lagrangian, long known to provide its most compact expression as well as the most efficient generation of the graviton vertices, is taken as the starting point for discussing General…
This thesis studies modified theories of gravity from a geometric viewpoint. We review the motivations for considering alternatives to General Relativity and cover the mathematical foundations of gravitational theories in Riemannian and…
A gravitational field model based on two symmetric tensors, $g_{\mu \nu}$ and $\tilde{g}_{\mu \nu}$, is presented. In this model, new matter fields are added to the original matter fields, motivated by an additional symmetry…
General relativity is a set of physical and geometric principles, which lead to a set of (Einstein) field equations that determine the gravitational field, and to the geodesic equations that describe light propagation and the motion of…
The so-called unimodular version of General Relativity is revisited. Unimodular gravity is constructed by fixing the determinant of the metric, what leads to the trace-free part of the equations instead of the usual Einstein field…
We present a framework that reformulates gravitational lensing as an optical phenomenon governed by an effective refractive index, enabling exploration of modified gravity theories using undergraduate-level mathematics and optics. After…
In the usual matrix-model approach to random discretized two-dimensional manifolds, one introduces n Ising spins on each cell, i.e. a discrete version of 2D quantum gravity coupled to matter with a central charge n/2. The matrix-model…
We provide a novel model of gravity by using adjoint frame fields in four dimensions. It has a natural interpretation as a gravitational theory of a complex metric field, which describes interactions between two real metrics. The classical…
Quantum Electrodynamics (QED) has been so successful a theory that it is taken as a model for the production of further quantum theories. However, when the prescription for quantising electromagnetic interactions that so successfully…
{\it If gravity is a metric field by Einstein, it is a Higgs field.} Gravitation theory meets spontaneous symmetry breaking in accordance with the Equivalence Principle reformulated in the spirit of Klein-Chern geometries of invariants. In…
The crucial but undocumented Dolan-McCrea variational method is richly applied. Using the said method, we analytically derived a field equation comprising entirely of geometric structures and we investigate how effectively it describes…
The configuration space of general relativity is superspace - the space of all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued that the configuration space for gravity should be conformal superspace - the space of…
That preferred-frame theory accounts for special relativity and reduces to it if the gravitation field cancels. Starting from an interpretation of gravity as a pressure force, it is based on just one scalar field. This scalar gives the…
In the multiscalar-metric frameworks, the issues of the vacuum energy/cosmological constant (CC) screening due to the Weyl-scale enhancement of the Diff gauge symmetry, along with emergence of the massive dark gravity components through the…
Based on the Generalized Principle of Inertia, which states that: \emph{An inanimate object moves freely, that is, with zero acceleration, in its own spacetime, whose geometry is determined by all of the forces affecting it,} we geometrize…