Metric-Affine Myrzakulov Gravity Theories

In this paper, we review the so-called Myrzakulov Gravity models (MG-N, with N = I, II, …, VIII) and derive their respective metric-affine generalizations (MAMG-N), discussing also their particular sub-cases. The field equations of the theories are obtained by regarding the metric tensor and the general affine connection as independent variables. We then focus on the case in which the function characterizing the aforementioned metric-affine models is linear and consider a Friedmann-Lemaître–Robertson–Walker background to study cosmological aspects and applications. Historical motivation for this research is thoroughly reviewed and specific physical motivations are provided for the aforementioned family of alternative theories of gravity.

On the violation of the invariance of the light speed in theoretical investigations

In this review, we analyze some of the most important theoretical attempts to challenge the invariance of the light speed postulated by the Special Theory of Relativity (STR). Most of those studies, however, show that STR has great stability with respect to various kinds of modifications in its axioms. This stability probably is due to the fact that in these modifications there is no so much a violation of the physical postulate of the invariance of the speed of light, as its mathematical expansion in the form of making resort to a more general affine space. In these modifications, we refer to more general transformation groups, including scale transformation of the speed of light and time [Formula: see text], [Formula: see text].

The natural operators of general affine connections into general affine connections

We reduce the problem of describing all \(\mathcal{M} f_m\)-natural operators transforming general affine connections on \(m\)-manifolds into general affine ones to the known description of all \(GL(\mathbf{R}^m)\)-invariant maps \(\mathbf{R}^{m*}\otimes \mathbf{R}^m\to \otimes^k\mathbf{R}^{m*}\otimes\otimes ^k\mathbf{R}^m\) for \(k=1,3\).