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

Understand

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.