  It is shown that using the relativistic field theory of gravity (RTG) and
measured value of $\Omega_{tot}$ one can obtain the upper limit on the graviton
mass with 95%C.L.: $m\leq 1.6\cdot 10^{-66}$ [g]; within the $(1\sigma)$ range
its probable value is $m_{g}= 1.3\cdot 10^{-66}$ [g]. It is pointed out that
according to RTG the presence of the quintessence is necessary to explain the
Universe accelerated expansion. Experimental data on the Universe age and dark
matter density allow one to determine the range of possible values of the $\nu$
parameter in the equation of quintessence state and indicate characteristic
time, which corresponds to the beginning and cessation of the accelerated
expansion epoch, as well as the time period of the maximal expansion, which
corresponds to the half-period of the oscillatory evolution of the Universe.
