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

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