Variety of cosmic acceleration models from massive F(R) bigravity

We study the accelerating cosmology in massive F(R) bigravity via the reconstruction scheme. The consistent solution of the FM equations is presented: it includes Big and Little Rip, quintessence, de Sitter and decelerating universes described by the physical g metric while the corresponding solution of the universe described by the reference f metric is also found. It is demonstrated that in general the cosmological singularities of g metric are not always manifested as cosmological singularities of the reference f metric. We give two consistent ways to describe the Big and Little Rip, quintessence, de Sitter and decelerating universes. In one of the consistent solutions, the two metrics g and f coincide with each other, which may indicate the connection with the convenient single metric background formulation. For another solution, where two metrics g and f do not coincide with each other, there always appears super-luminal mode.