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The concept of smooth deformations of a Riemannian manifolds, recently evidenced by the solution of the Poincar\'e conjecture, is applied to Einstein's gravitational theory and in particular to the standard FLRW cosmology. We present a…
Our conventional system of physical units is based on local or microscopic {\it dimensional} quantities which are {\it defined}, for convenience or otherwise aesthetic reasons, to be spacetime-independent. A more general choice of units may…
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…
Suggested theory involves a drastic revision of a role of local internal symmetries in physical concept of curved geometry. Under the reflection of fields and their dynamics from Minkowski to Riemannian space a standard gauge principle of…
We show that the effective field equations for a recently formulated polynomial affine model of gravity, in the sector of a torsion-free connection, accept general Einstein manifolds---with or without cosmological constant---as solutions.…
Various candidates of quantum gravity such as string theory, loop quantum gravity and black hole physics all predict the existence of a minimum observable length which modifies the Heisenberg uncertainty principle to so-called Generalized…
It is shown that introducing the quantum effects using deBroglie--Bohm theory in the canonical formulation of gravity would change the constraints algebra. The new algebra is derived and shown that it is the clear projection of general…
We argue that the structure general relativity (GR) as a theory of affine defects is deeper than the standard interpretation as a metric theory of gravitation. Einstein-Cartan theory (EC), with its inhomogenous affine symmetry, should be…
We speculate on the role of relativistic versions of delayed differential equations in fundamental physics. Relativistic invariance implies that we must consider both advanced and retarded terms in the equations, so we refer to them as…
We describe the cyclic $L_{\infty}$-algebra formulation of classical general relativity without matter fields in the Einstein-Cartan-Palatini formalism. Using Drinfel'd twist deformation techniques, we define a noncommutative version of the…
A systematic study of deformations of four-dimensional Einsteinian space-times embedded in a pseudo-Euclidean space $E^N$ of higher dimension is presented. Infinitesimal deformations, seen as vector fields in $E^N$, can be divided in two…
We argue that generic off-diagonal vacuum and nonvacuum solutions for Einstein manifolds mimic physical effects in modified gravity theories (MGTs) and encode certain models of the $f(R,T,...)$, Ho\v{r}ava type with dynamical Lorentz…
We use the covariant formulation proposed in Tattersall et al (2017) to analyse the structure of linear perturbations about a spherically symmetric background in different families of gravity theories, and hence study how quasi-normal modes…
Generic relevant deformations of Einstein's gravity theory contain additional degrees of freedom that have a multi-facetted stabilization dynamics on curved spacetimes. We show that these relevant degrees of freedom are self-protected…
A family of diffeomorphism-invariant Seiberg--Witten deformations of gravity is constructed. In a first step Seiberg--Witten maps for an SO(1,3) gauge symmetry are obtained for constant deformation parameters. This includes maps for the…
In this talk, I present a theory of quantum gravity beyond Einstein. The theory is established based on spinnic and scaling gauge symmetries by treating the gravitational force on the same footing as the electroweak and strong forces. A…
We analyze 2+1-dimensional gravity in the framework of quantum gauge theory. We find that Einstein gravity has a trivial physical subspace which reflects the fact that the classical solution in empty space is flat. Therefore we study…
It is well known that Einstein's equations assume a simple polynomial form in the Hamiltonian framework based on a Yang-Mills phase space. We re-examine the gravitational dynamics in this framework and show that {\em time} evolution of the…
The fundamental field equations in modified gravity (including general relativity; massive and bimetric theories; Ho\vrava-Lifshits, HL; Einstein--Finsler gravity extensions etc) posses an important decoupling property with respect to…
We show that various dynamical gauge theories in two, three and four dimensions, obtained as Manin deformations of topological Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) theories, are equivalent to gravitational theories. Since gravity…