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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…
Gravitation as a fundamental interaction that governs all phenomena at large and very small scales, but still not well understood at a quantum level, is a missing cardinal link to unification of all physical interactions. Problems of the…
General Relativity (GR) exists in different formulations, which are equivalent in pure gravity. Once matter is included, however, observable predictions generically depend on the version of GR. In order to quantify the resulting ambiguity,…
Gravitoelectromagnetic analogies are somewhat ubiquitous in General Relativity, and they are often used to explain peculiar effects of Einstein's theory of gravity in terms of familiar results from classical electromagnetism. Perhaps, the…
Recently a class of alternative theories of gravity which goes under the name f(R) gravity, has received considerable attention, mainly due to its interesting applications in cosmology. However, the phenomenology of such theories is not…
Starting from the original Einstein action, sometimes called the Gamma squared action, we propose a new setup to formulate modified theories of gravity. This can yield a theory with second order field equations similar to those found in…
A specific theoretical framework is important for designing and conducting an experiment, and for interpretation of its results. The field of gravitational physics is expanding, and more clarity is needed. It appears that some popular…
Modified gravity (MOG) is a covariant, relativistic, alternative gravitational theory whose field equations are derived from an action that supplements the spacetime metric tensor with vector and scalar fields. Both gravitational (spin 2)…
This review presents a comprehensive overview of Myrzakulov gravity, highlighting key developments and significant results shaping the theory. It examines the foundational principles, field equations, and the role of non-metricity and…
A modified theory of gravity, avoiding singularities in the standard theory of gravitation, has been developed by Hess & Greiner, known as the pseudo-complex theory of gravitation. The pc-GR theory shows remarkable observational differences…
In a recent paper [1], it was introduced a new class of gravitational theories with two local degrees of freedom. The existence of these theories apparently challenges the distinctive role of general relativity as the unique non-linear…
We review recent progress in the construction of modified gravity models as alternatives to dark energy as well as the development of cosmological tests of gravity. Einstein's theory of General Relativity (GR) has been tested accurately…
In the present paper we will investigate the relation between scalar-tensor theory and $f(R)$ theories of gravity. Such studies have been performed in the past for the metric formalism of $f(R)$ gravity; here we will consider mainly the…
The teleparallel formulation of gravity theories reveals close structural analogies to electrodynamics, which are more hidden in their usual formulation in terms of the curvature of spacetime. We show how every locally Lorentz invariant…
The M\"ossbauer rotor effect recently gained a renewed interest due to the discovery and explanation of an additional effect of clock synchronization which has been missed for about 50 years, i.e. starting from a famous book of Pauli, till…
General relativity is highly successful in explaining a wide range of gravitational phenomena including the gravitational waves emitted by binary systems and the shadows cast by supermassive black holes. From a modern perspective the theory…
A very short, non-technical review of the main problems which are presently open in the context of the gravitational theory and of its cosmological applications, and which are currently under investigation and deep discussion. We will talk…
In this review we present a thoroughly comprehensive survey of recent work on modified theories of gravity and their cosmological consequences. Amongst other things, we cover General Relativity, Scalar-Tensor, Einstein-Aether, and Bimetric…
The assumption that matter charges and currents could generate fields, which are called, by analogy with electromagnetism, gravitoeletric and gravitomagnetic fields, dates from the origins of General Relativity (GR). On the other hand, the…
We summarize theoretical and experimental work on tests of CPT and local Lorentz symmetry in gravity. Recent developments include extending the effective field theory framework into the nonlinear regime of gravity.