  We present a simple procedure to obtain all de Sitter solutions in the
ghost-free massive gravity theory by using the Gordon ansatz. For these
solutions the physical metric can be conveniently viewed as describing a
hyperboloid in 5D Minkowski space, while the flat reference metric depends on
the Stuckelberg field $T(t,r)$ that satisfies the equation
$(\partial_t{T})^2-(\partial_r T)^2=1$. This equation has infinitely many
solutions, hence there are infinitely many de Sitter vacua with different
physical properties. Only the simplest solution with $T=t$ has been previously
studied since it is manifestly homogeneous and isotropic, but it is unstable.
However, other solutions could be stable. We require the timelike isometry to
be common for both metrics, and this gives physically distinguished solutions
since only for them the canonical energy is time-independent. We conjecture
that these solutions minimize the energy and are therefore stable. We also show
that in some cases solutions can be homogeneous and isotropic in a non-manifest
way such that their symmetries are not obvious. All of this suggests that the
theory may admit viable cosmologies.
