The RTG is able to solve some important cosmological problems. It does not contain the cosmological singularity and derives the flatness of the global spacetime from the field equations. The antigravitation produced by the massive graviton in the strong gravitational field solves the problem of the source of the initial expansion and allows escaping the relics creation. However, the problems of the horizon and the present accelerated expansion of the universe remain. The former is solvable in the framework of the oscillation paradigm. The RTG admits only closed evolutional scenario in virtue of the causality principle and thereby the causal connections with the extremely distant domains can result from the previous cycles of the oscillation (remind that there is no the singularity in the RTG). However, the problem of the accelerated expansion needs some additional hypothesis. The appropriate modification of the RTG Lagrangian is awkward because the structure of its massive part is defined by the polarization properties of the gravitational field. The alternative way is the modification of the energy-momentum tensor due to inclusion of the so-called quintessence term with the state parameter lying within the limits of the strong and weak energy conditions that causes the repulsion and, as a result, the accelerated expansion.