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In this work we give special attention to the bimetric theory of gravitationwith massive gravitons proposed by Visser in 1998. In his theory, a priorbackground metric is necessary to take in account the massive term. Although inthe great part of the astrophysical studies the Minkowski metric is the bestchoice to the background metric, it is not possible to consider this metric incosmology. In order to keep the Minkowski metric as background in this case, wesuggest an interpretation of the energy-momentum conservation in Visser'stheory, which is in accordance with the equivalence principle and recoversnaturally the special relativity in the absence of gravitational sources.Although we do not present a general proof of our hypothesis we show itsvalidity in the simple case of a plane and dust-dominated universe, in whichthe `massive term' appears like an extra contribution for the energy density.

The conservation of energy-momentum and the mass for the graviton