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Gravitational theories with fixed background fields break diffeomorphism invariance. This breaking can be spontaneous or explicit. A brief summary of the main consequences of these types of breaking is presented.
To explain the recently reported large-scale spatial variations of the fine structure constant $\alpha$, we apply some models of curvature-nonlinear multidimensional gravity. Under the reasonable assumption of slow changes of all quantities…
Possible models of modified gravity are being extensively studied now, with most phenomenological motivations coming from puzzles and tensions in cosmology due to a natural desire to better fit the known and newly coming data. At the same…
General Relativity (GR) is a phenomenologically successful theory that rests on firm foundations, but has not been tested on cosmological scales. The advent of dark energy (and possibly even the requirement of cold dark matter), has…
A broad class of generalized Einstein's gravity can be cast into Einstein's gravity with a minimally coupled scalar field using suitable conformal rescaling of the metric. Using this conformal equivalence between the theories, we derive the…
Einstein gravitation theory can be extended by preserving its geometrical nature but changing the relation between curvature and energy-momentum tensors. This change accounts for radiative corrections, replacing the Newton gravitation…
Alternative theories of gravity predict the presence of massive scalar, vector, and tensor gravitational wave modes in addition to the standard massless spin~2 graviton of general relativity. The deflection and frequency shift effects on…
We discuss some effects induced by quantum field fluctuations on mass, inertia and gravitation. Recalling the problem raised by vacuum field fluctuations with respect to inertia and gravitation, we show that vacuum energy differences, such…
The quantum gravity is formulated based on principle of local gauge invariance. The model discussed in this paper has local gravitational gauge symmetry and gravitational field appears as gauge field. The problems on quantization and…
A generalization of Newtonian gravitation theory is obtained by a suitable limiting procedure from the ADM action of general relativity coupled to a mass-point. Three particular theories are discussed and it is found that two of them are…
In this lecture, I explain the gauge-invariant formulation for perturbations of background spacetimes with untwisted homologous Einstein fibres, which include lots of practically important spacetimes such as static black holes, static black…
Some problems of spontaneous and gravitational baryogenesis are discussed. Gravity modification due to the curvature dependent term in gravitational baryogensis scenario is considered. It is shown that the interaction of baryonic fields…
Cosmological observations indicate that the Einstein equation may not be entirely correct to describe gravity. However, numerous modifications of these equations usually do not affect foundations of the theory. In this paper two important…
A new approach to gravitational gauge-invariant perturbation theory begins from the fourth-order Einstein-Ricci system, a hyperbolic formulation of gravity for arbitrary lapse and shift whose centerpiece is a wave equation for curvature. In…
The gravitational wave solutions obtained from a perturbation about conformally flat backgrounds in Einstein gravity are investigated. A perturbation theory analysis of the Lesame, Ellis and Dunsby results, based on a covariant approach,…
It has been speculated that gravity could be an emergent phenomenon, with classical general relativity as an effective, macroscopic theory, valid only for classical systems at large temporal and spatial scales. As in classical continuum…
We study the stability of fracton gravity, a variant of linearized gravity where the gauge symmetry is restricted to longitudinal diffeomorphisms. These transformations can be connected to a spacetime generalization of dipole symmetry,…
We consider the cosmology where some function f(G) of the Gauss-Bonnet term G is added to the gravitational action to account for the late-time accelerating expansion of the universe. The covariant and gauge invariant perturbation equations…
The Gauss-Bonnet invariant connects foundational aspects of geometry with physical phenomena in a variety of ways. Teleparallel gravity offers a novel direction in which to use the Gauss-Bonnet invariant to go beyond standard cosmology. In…
We discuss possible variations of the effective gravitational constant with length scale, predicted by most of alternative theories of gravity and unified models of physical interactions. After a brief general exposition, we review in more…