  In bigravity, when taking into account the potential existence of matter
fields minimally coupled to the second gravitation sector, the dynamics of our
Universe depends on some matter that cannot be observed in a direct way. In
this paper, we assume the existence of a Noether symmetry in bigravity
cosmologies in order to constrain the dynamics of that matter. By imposing this
assumption we obtain cosmological models with interesting phenomenology. In
fact, considering that our universe is filled with standard matter and
radiation, we show that the existence of a Noether symmetry implies that either
the dynamics of the second sector decouples, being the model equivalent to
General Relativity, or the cosmological evolution of our universe tends to a de
Sitter state with the vacuum energy in it given by the conserved quantity
associated with the symmetry. The physical consequences of the genuine
bigravity models obtained are briefly discussed. We also point out that the
first model, which is equivalent to General Relativity, may be favored due to
the potential appearance of instabilities in the second model.
