  We propose that the Universe is filled with a massive vector field,
non-minimally coupled to gravitation. The field equations of the model are
consistently derived and their application to cosmology is considered. The
Friedmann equations acquire an extra dark-energy component, which is
proportional to the mass of the vector particle. This leads to a late-time
accelerated de Sitter type expansion. The free parameters of the model
(gravitational coupling constants and initial value of the cosmological vector
field) can be estimated by using the PPN solar system constraints. The mass of
the cosmological massive vector particle, which may represent the main
component of the Universe, is of the order of 10^-63 g.
