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

Abstract

In this work we give special attention to the bimetric theory of gravitation with massive gravitons proposed by Visser in 1998. In his theory, a prior background metric is necessary to take in account the massive term. Although in the great part of the astrophysical studies the Minkowski metric is the best choice to the background metric, it is not possible to consider this metric in cosmology. In order to keep the Minkowski metric as background in this case, we suggest an interpretation of the energy–momentum conservation in Visser’s theory, which is in accordance with the equivalence principle and recovers naturally the special relativity in the absence of gravitational sources. Although we do not present a general proof of our hypothesis we show its validity in the simple case of a plane and dust-dominated universe, in which the “massive term” appears like an extra contribution for the energy density.