  Following the path of minimalism in alternative theories of gravity, we
construct the "Minimal Theory of Bigravity" (MTBG), a theory of two interacting
spin-2 fields that propagates only four local degrees of freedom instead of the
usual seven ones and that allows for the same homogeneous and isotropic
cosmological solutions as in Hassan-Rosen bigravity (HRBG). Starting from a
precursor theory that propagates six local degrees of freedom, we carefully
choose additional constraints to eliminate two of them to construct the theory.
Investigating the cosmology of MTBG, we find that it accommodates two different
branches of homogeneous and isotropic background solutions, equivalent on-shell
to the two branches that are present in HRBG. Those branches in MTBG differ
however from the HRBG ones at the perturbative level, are both perfectly
healthy and do not exhibit strong coupling issues nor ghost instabilities. In
the so-called self-accelerating branch, characterized by the presence of an
effective cosmological constant, the scalar and vector sectors are the same as
in General Relativity (GR). In the so-called normal branch, the scalar sector
exhibits non-trivial phenomenology, while its vector sector remains the same as
in GR. In both branches, the tensor sector exhibits the usual HRBG features: an
effective mass term and oscillations of the gravitons. Therefore MTBG provides
a stable nonlinear completion of the cosmology in HRBG.
