  We describe scalar-bimetric theories where the dynamics of the Universe are
governed by two separate metrics, each with an Einstein-Hilbert term. In this
setting, the baryonic and dark matter components of the Universe couple to
metrics which are constructed as functions of these two gravitational metrics.
The scalar field, contrary to dark energy models, does not have a potential
whose role is to mimic a late-time cosmological constant. The late-time
acceleration of the expansion of the Universe can be easily obtained at the
background level in these models by appropriately choosing the coupling
functions appearing in the decomposition of the vierbeins for the baryonic and
dark matter metrics. We explicitly show how the concordance model can be
retrieved with negligible scalar kinetic energy. This requires the scalar
coupling functions to show variations of order unity during the accelerated
expansion era. This leads in turn to deviations of order unity for the
effective Newton constants and a fifth force that is of the same order as
Newtonian gravity, with peculiar features. The baryonic and dark matter
self-gravities are amplified although the gravitational force between baryons
and dark matter is reduced and even becomes repulsive at low redshift. This
slows down the growth of baryonic density perturbations on cosmological scales,
while dark matter perturbations are enhanced. In our local environment, the
upper bound on the time evolution of Newton's constant requires an efficient
screening mechanism that both damps the fifth force on small scales and
decouples the local value of Newton constant from its cosmological value. This
cannot be achieved by a quasi-static chameleon mechanism, and requires going
beyond the quasi-static regime and probably using derivative screenings, such
as Kmouflage or Vainshtein screening, on small scales.
