Isotropy theorem for arbitrary-spin cosmological fields

We show that the energy-momentum tensor of homogeneous fields of arbitrary spin in an expanding universe is always isotropic in average provided the fields remain bounded and evolve rapidly compared to the rate of expansion. An analytic expression for the average equation of state is obtained for Lagrangians with generic power-law kinetic and potential terms. As an example we consider the behavior of a spin-two field in the standard Fierz-Pauli theory of massive gravity. The results can be extended to general space-time geometries for locally inertial observers.