The evolution of universe in the two-scalar theory

We generalize f(R,T) gravity into the two-scalar theory that includes two independent scalar fields by the variational method, and we derive its field equations in Einstein frame using conformal transformation. Based on Friedmann equations and Raychaudhuri equation, with a consideration of the cosmic content as its perfect-fluid form, a further discussion leads us to an accelerated expanding condition of universe. In the two-scalar theory, universe has two states which are the accelerated expansion and decelerated contraction, and it has three stages during its evolution. The first and third stages are in the accelerated expanding state, and the second stage is in the decelerated contracting state. The third stage represents the present universe and it tends to become a dust universe.