  In this work, we explore some cosmological implications of the model proposed
by M. Visser in 1998. In his approach, Visser intends to take in account mass
for the graviton by means of an additional bimetric tensor in the Einstein's
field equations. Our study has shown that a consistent cosmological model
arises from Visser's approach. The most interesting feature is that an
accelerated expansion phase naturally emerges from the cosmological model, and
we do not need to postulate any kind of dark energy to explain the current
observational data for distant type Ia supernovae (SNIa).
