  It was shown, that the presence of the so-called X-matter with an equation of
state, which lies between limits of the strong and weak energy conditions,
allows the variety of the cosmological scenarios in the relativistic theory of
gravity. In spite of the fixed negative sign of the cosmological term in the
field equations with massive graviton, it is possible to obtain the solutions
with accelerated and complicated loitering expansion of the universe. The
numerical estimation of the universe's age agrees with the modern observational
data if the upper limit of the graviton's mass is 10^{-71} g
