  The present work deals with cosmological solutions in $f(R,T)$ gravity theory
for perfect fluid with constant equation of state ($\omega$). For a viable
cosmological solution $\omega$ is restricted to $\omega<\dfrac{1}{3}$. Also
depending on the sign of an arbitrary constant one has two possible solutions:
a finite universe model and an ever expanding model of the universe. Field
theoretic description of the model and possibility of a ghost scalar field has
been studied. Also, an equivalence with modified Chaplygin gas has been shown.
Finally, from the observational data it has been concluded that this model
represents an evolution of the universe from matter dominated phase to present
accelerating phase.
