  We study dynamics of Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime
based on the ghost-free bigravity theory. Assuming the coupling parameters
guaranteeing the existence of de Sitter space as well as Minkowski spacetime,
we find two stable attractors for spacetime with "twin" dust matter fields: One
is de Sitter accelerating universe and the other is matter dominated universe.
Although a considerable number of initial data leads to de Sitter universe, we
also find matter dominated universe or spacetime with a future singularity for
some initial data. The cosmic no-hair conjecture does not exactly hold, but the
accelerating expansion can be found naturally. The $\Lambda$-CDM model is
obtained as an attractor. We also show that the dark matter component in the
Friedmann equation, which originates from another twin matter, can be about 5
times larger than the baryonic matter, by choosing the appropriate coupling
constants.
