Graviton Mass, Quintessence and Oscillatory Character of the Universe Evolution

It is shown that using the relativistic field theory of gravity (RTG) and measured value of $\Omega_{\mbox{{\small tot}}}$ 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.