  We present a bimetric low-energy effective theory of fractional quantum Hall
(FQH) states that describes the topological properties and a gapped collective
excitation, known as Girvin-Macdonald-Platzman (GMP) mode. The theory consist
of a topological Chern-Simons action, coupled to a symmetric rank two tensor,
and an action \`a la bimetric gravity, describing the gapped dynamics of the
spin-$2$ GMP mode. The theory is formulated in curved ambient space and is
spatially covariant, which allows to restrict the form of the effective action
and the values of phenomenological coefficients. Using the bimetric theory we
calculate the projected static structure factor up to the $k^6$ order in the
momentum expansion. To provide further support for the theory, we derive the
long wave limit of the GMP algebra, the dispersion relation of the GMP mode,
and the Hall viscosity of FQH states. We also comment on the possible
applications to fractional Chern insulators, where closely related structures
arise. Finally, it is shown that the familiar FQH observables acquire a curious
geometric interpretation within the bimetric formalism.
