  The bigravity models coupled with two scalar fields are constructed. We show
that a wide class of the expansion history of the universe, especially
corresponding to dark energy and/or inflation, can be described by a solution
of the bigravity model. We discuss the stability of the solution and give the
conditions for the stability. We also explicitly construct a model which gives
a stable solution. By using the stable model, for an arbitrary evolution of the
universe expansion, we construct the Brans-Dicke like model which reproduces
the evolution.
