Metric-Affine Version of Myrzakulov $F(R,T,Q, {\cal T})$ Gravity and Cosmological Applications

TL;DR

This paper develops the field equations for a broad class of metric-affine gravity theories involving curvature, torsion, non-metricity, and matter couplings, and explores their cosmological implications through modified Friedmann equations.

Contribution

It extends Myrzakulov gravity to include additional geometric and matter terms, deriving full field equations and analyzing cosmological solutions in this generalized framework.

Findings

Derived the full set of field equations for the generalized theory.

Obtained modified Friedmann equations in a cosmological setting.

Presented solutions in the case of matter coupled to torsion with vanishing non-metricity.

Abstract

We derive the full set of field equations for the Metric-Affine version of the Myrzakulov gravity model and also extend this family of theories to a broader one. More specifically, we consider theories whose gravitational Lagrangian is given by $F(R,T,Q, {\cal T},{\cal D})$ where $T$, $Q$ are the torsion and non-metricity scalars, ${\cal T}$ is the trace of the energy-momentum tensor and ${\cal D}$ the divergence of the dilation current. We then consider the linear case of the aforementioned theory and assuming a cosmological setup we obtain the modified Friedmann equations. In addition, focusing on the vanishing non-metricity sector and considering matter coupled to torsion we obtain the complete set of equations describing the cosmological behaviour of this model along with solutions.