  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.
