Аннотация:A new model of Dark Energy is proposed within the flat FLRW model in RTG (Relativistic Theory of Gravitation). It is a global scalar field Φ with a quadratic potential, which ensures cosmologicalacceleration at present times and a bounce at late times. During the contraction stage, the growing Kasner-type anisotropy of Riemannian metrics will break a graviton-mass bounce mechanism near the Big Bang in the FLRW case. There is also a noncyclic scenario, with sufficiently small graviton-mass terms significant only at the final stage of expansion. After bounce, during the next compression epoch, anisotropy will increase, and the matter density will finally reach the Planck value.