  In the context of Finsler-Randers theory we consider, for a first time, the
cosmological scenario of the varying vacuum. In particular, we assume the
existence of a cosmological fluid source described by an ideal fluid and the
varying vacuum terms. We determine the cosmological history of this model by
performing a detailed study on the dynamics of the field equations. We
determine the limit of General Relativity, while we find new eras in the
cosmological history provided by the geometrodynamical terms provided by the
Finsler-Randers theory.
