Alternati̇ve gravi̇tati̇on theory f(R,T) and appli̇ed of thi̇s theory to cosmologi̇cal models

The problems of General Relativity about the late time acceleration of the universe have led to the emergence of some alternative gravitational theories. Nowadays, f (R) and f (R, T) theories are the most studied in the literature. In addition to explaining the late time acceleration of the universe without the need for dark energy, these theories complement other points where General Relativity is lacking. Although f (R,T) theories are a relatively new theory, it is widely studied in the literature. One of the main reasons for this is that the action equation is due to the trace of the energy-momentum tensor T. This commitment leads to different field equations for each L_m to be selected. This shows that quantum effects can be found in the field equation. In this study, firstly, the theory of general relativity and the situations in which it suffers are mentioned. Afterward, the structure of f (R) and f (R,T) theories and their solutions to these problems are mentioned and finally, the similarities or differences are examined by analyzing the solutions in Bianchi type I and V models in order to compare each of the three theories with each other.