  The basic aim of this manuscript is to investigate the cosmological solutions
in the context of the modified $f(R, T)$ theory of gravity, where $R$ is the
Ricci scalar and $T$ is the trace of the energy-momentum tensor. For our
current work, we consider the Friedmann-Robertson-Walker space-time for finding
the solutions of field equations. We investigate the nature of universe by
considering acceleration expansion of universe, ultra relativistic universe,
sub-relativistic universe, dust universe, radiation universe, stiff universe.
Moreover, we apply the power law technique by taking two different $f(R, T)$
gravity models to observe the expanding nature of the universe. The bouncing
scenario is also discussed by choosing some particular values of the model
parameters and observed the energy conditions, which are satisfied for a
successful bouncing model. It is also concluded that some solutions in $f(R,
T)$ theory of gravity supports the concept of exotic matter and accelerated
expansion of the universe due to a large amount of negative pressure.
