  We investigate the cosmological reconstruction in modified f(R,T) gravity,
where R is the Ricci scalar and T the trace of the stress-energy tensor.
Special attention is attached to the case in which the function f is given by f
(R, T) = f1 (R) + f2 (T). The use of auxiliary scalar field is considered with
two known examples for the scale factor corresponding to an expanding universe.
In the first example, where ordinary matter is usually neglected for obtaining
the unification of matter dominated and accelerated phases with f(R)gravity, it
is shown in this paper that this unification can be obtained without neglect
ordinary matter. In the second example, as in f(R)gravity, model of f(R, T)
gravity with transition of matter dominated phase to the acceleration phase is
obtained. In both cases, linear function of the trace is assumed for f2(T) and
it is obtained that f1(R) is proportional to a power of R with exponents
depending on the input parameters.
