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Einstein's equations in a tetrad formulation are derived from a linear theory in flat spacetime with an asymmetric potential using free field gauge invariance, local Lorentz invariance and universal coupling. The gravitational potential can…
Gauge theories and perturbative gravity in four dimensions are governed by a tower of infinite-dimensional symmetries which arise from tree-level soft theorems. However, aside from the leading soft theorems which are all-loop exact,…
The universal character of the gravitational interaction provided by the equivalence principle motivates a geometrical description of gravity. The standard formulation of General Relativity \`a la Einstein attributes gravity to the…
Solutions to the field equations of the Nonsymmetric Gravitational Theory with $g_[i0] = 0$ are obtained for the homogeneous, plane-symmetric, time-dependent case, both in vacuum and in the presence of a perfect fluid. Cosmological…
From a purely none-general relativistic standpoint, we solve the empty space Poisson equation ($\nabla^{2}\Phi=0$) for an azimuthally symmetric setting, i.e., for a spinning gravitational system like the Sun. We seek the general solution of…
This article reviews basic construction and cosmological implications of a power-counting renormalizable theory of gravitation recently proposed by Horava. We explain that (i) at low energy this theory does not exactly recover general…
The evolution of a generally covariant theory is under-determined. One hundred years ago such dynamics had never before been considered; its ramifications were perplexing, its future important role for all the fundamental interactions under…
A thorough study and analysis on the conceptual foundations of unimodular gravity shows that this theory is essentially general relativity disguised as unimodular relativity in the literature. The main reason for this dilemma is accepting…
We argue that more cosmological solutions in massive gravity can be obtained if the metric tensor and the tensor $\Sigma_{\mu\nu}$ defined by St\"{u}ckelberg fields take the homogeneous and isotropic form. The standard cosmology with matter…
It is believed that gravity will be explained in the framework of the existing quantum theory when one succeeds in eliminating divergencies at large momenta or small distances (although the phenomenon of gravity has been observed only at…
The possibility that a classical space-time and quantum matter cohabit at the deepest level, i.e. the possibility of having a fundamental and not phenomenological semiclassical gravity, is often disregarded for lack of a good candidate…
We study anisotropic cosmology in Ho\v{r}ava's gravity theory and obtain Kasner type solutions, valid for any number d of spatial dimensions. The corresponding exponents satisfy two relations, one involving the marginal coupling \lambda.…
We recall a classical theory of torsion gravity with an asymmetric metric, sourced by a Nambu-Goto + Kalb-Ramond string . We explain why this is a significant gravitational theory, and in what sense classical general relativity is an…
We investigate a possible unified theory of all interactions which is based only on fundamental spinor fields. The vielbein and metric arise as composite objects. The effective quantum gravitational theory can lead to a modification of…
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…
In the framework of the recently proposed models of massive gravity, defined with respect to a de Sitter reference metric, we obtain new homogeneous and isotropic solutions for arbitrary cosmological matter and arbitrary spatial curvature.…
We couple a conformal scalar field in (2+1) dimensions to Einstein gravity with torsion. The field equations are obtained by a variational principle. We could not solve the Einstein and Cartan equations analytically. These equations are…
After a brief summary of the Newton-Cartan theory in a form which emphasizes its close analogy to general relativity, we illustrate the theory with selective applications in cosmology. The geometrical formulation of this nonrelativistic…
The spatially homogeneous, isotropic Standard Cosmological Model appears to describe our Universe reasonably well. However, Einstein's equations allow a much larger class of cosmological solutions. Theorems originally due to Penrose and…
We drastically simplify the problem of linearizing a general higher-order theory of gravity. We reduce it to the evaluation of its Lagrangian on a particular Riemann tensor depending on two parameters, and the computation of two derivatives…