  Vector fields in the expanding Universe are considered within the
multidimensional theory of General Relativity.
  Vector fields in general relativity form a three-parametric variety. Our
consideration includes the fields with a nonzero covariant divergence.
Depending on the relations between the particular parameters and the symmetry
of a problem, the vector fields can be longitudinal and/or transverse,
ultrarelativistic (i.e. massless) or nonrelativistic (massive), and so on.
  The longitudinal and transverse vector fields are considered separately in
detail in the background of the de Sitter cosmological metric. In most cases
the field equations reduce to Bessel equations, and their temporal evolution is
analyzed analytically. The energy-momentum tensor of the most simple zero-mass
longitudinal vector fields enters the Einstein equations as an additive to the
cosmological constant. In this case the de Sitter metric is the exact solution
of the Einstein equations. Hence, the most simple zero-mass longitudinal vector
field pretends to be an adequate tool for macroscopic description of dark
energy as a source of the expansion of the Universe at a constant rate. The
zero-mass vector field does not vanish in the process of expansion. On the
contrary, massive fields vanish with time. Though their amplitude is falling
down, the massive fields make the expansion accelerated.
  The macroscopic analysis of vector fields in cosmology gives up the hope that
the major puzzle -- attraction between individual objects and expansion of the
Universe as a whole -- can be solved within the Einstein's theory of general
relativity.
