Metric-affine Myrzakulov gravity and its generalizations

Since the discovery of cosmic acceleration, modified gravity theories play an important role in the modern cosmology. In particular, the well-known F(R) - theories reached great popularity motivated by the easier formalism and by the prospect to find a final theories of gravity for the dark scenarios. In the present work, we study some generalizations of F(R), F(T) and F(Q) gravity theories, where $R, T, Q$ are the Ricci, torsion and nonmetricity scalars. At the beginning, we briefly review the formalism of such theories. Then, we will consider one of their generalizations, the so-called Myrzakulov F(R,T) gravity theory or the MG-I theory. The point-like Lagrangian is explicitly presented. Based on this Lagrangian, the field equations of MG-I are found. For the specific model $F(R,T)=\mu R+\nu T,$ the corresponding exact solutions are derived. Furthermore, we will consider the physical quantities associated to such solutions and we will find how for some values of the parameters the expansion of our universe can be accelerated without introducing any dark component. Finally, some metric-affine Myrzakulov gravity theories with and without boundary term scalars are presented.