  The bimetric generalization of general relativity has been proven to be able
to give an accelerated background expansion consistent with observations. Apart
from the energy densities coupling to one or both of the metrics, the expansion
will depend on the cosmological constant contribution to each of them, as well
as the three parameters describing the interaction between the two metrics.
Even for fixed values of these parameters can several possible solutions, so
called branches, exist. Different branches can give similar background
expansion histories for the observable metric, but may have different
properties regarding, for example, the existence of ghosts and the rate of
structure growth. In this paper, we outline a method to find viable solution
branches for arbitrary parameter values. We show how possible expansion
histories in bimetric gravity can be inferred qualitatively, by picturing the
ratio of the scale factors of the two metrics as the spatial coordinate of a
particle rolling along a frictionless track.
