Metric-Affine Myrzakulov Gravity Theories

Abstract

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.

Three-dimensional non-relativistic extended supergravity with cosmological constant

“…See, e.g.,[88] for a recent review on non-Riemannian structures and applications in (super)gravity. Besides, we refer the reader to, e.g.,[89][90][91][92][93] for further implications of a non-vanishing torsion and non-Riemannian structures in gravity and supergravity theories.…”

Metric-Affine Vector-Tensor Correspondence and Implications in $F(R,T,Q,\mathcal{T},\mathcal{D})$ gravity

“…The other are subcases. Such theories have been generalized to the Metric-Affine framework in [22,23], including also a dependence on the divergence of the dilation current D, the latter being a trace of the hypermomentum tensor [38][39][40], in F . In Table 1 the reader can find a summary of the Metric-Affine Myrzakulov Gravity (MAMG) theories that have been developed and analyzed (L m in Table 1 denotes the matter action).…”

“…Such theories have been analyzed mainly in four spacetime dimension and provided relevant applications in the cosmological context. For an exhaustive review of cosmological features of (MA)MG models and the way in which they offer solutions to diverse issues in the context of cosmology we refer the reader to [23] and references therein. We shall now focus on F (R, T, Q, T ) gravity in some particular cases in which the function F is linear in R, Q, and T , in vacuum, to highlight some implications of the previously discussed quadratic formulation in such model.…”

“…The masses of these Proca fields and the strengths of their interactions depend on the parameters of the theory. Continuing, in Section 5 we provide implications of the formulation to the case of (linear) F (R, T, Q, T , D) gravity, also known in the literature as Metric-Affine Myrzakulov Gravity VIII (MAMG-VIII), in vacuum, see, e.g., [22] and the recent review [23]. Section 6 is devoted to some final remarks and possible future developments.…”

Cosmology of Metric‐Affine R+βR2$R + \beta R^2$ Gravity with Pure Shear Hypermomentum

“…Several studies on cosmological aspects have been performed, especially in the last years, by considering the large class of MAG theories (see, e.g., refs. [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44]). 1 Here we shall consider f (R) gravity in the metric-affine setup.…”