LAUSR

In literature, there is a model of modified gravity in which the matter Lagrangian is coupled to the geometry via trace of the stress–energy–momentum tensor T = Tμμ. This type of modified gravity is denoted f(R,T) in which R is Ricci scalar R = Rμμ. We extend manifestly this model to include the higher derivative term □R. We derived equations of motion (EOM) for the model by starting from the basic variational principle. Later we investigate FLRW cosmology for our model. We show that de Sitter (dS) solution is unstable for a generic type of f(R,□R,T) model. Furthermore we investigate an inflationary scenario based on this model. A graceful exit from inflation is guaranteed in this type of modified gravity.