  One of the fundamental open questions in cosmology is whether we can regard
the universe evolution without singularity like a Big Bang or a Big Rip. This
challenging subject stimulates one to regard a nonsingular universe in the far
past with an arbitrarily large vacuum energy. Considering the high energy
regime in the cosmic history, it is believed that Einstein gravity should be
corrected to an effective energy dependent theory which could be acquired by
gravity's rainbow. On the other hand, employing massive gravity provided us
with solutions to some of the long standing fundamental problems of cosmology
such as cosmological constant problem and self acceleration of the universe.
Considering these aspects of gravity's rainbow and massive gravity, in this
paper, we initiate studying FRW cosmology in the massive gravity's rainbow
formalism. At first, we show that although massive gravity modifies the FRW
cosmology, but it does not itself remove the big bang singularity. Then, we
generalize the massive gravity to the case of energy dependent spacetime and
find that massive gravity's rainbow can remove the early universe singularity.
We bring together all the essential conditions for having a nonsingular
universe and the effects of both gravity's rainbow and massive gravity
generalizations on such criteria are determined.
