Generalization of Abelian Gauge Symmetry and the Dark Matter and Energy
  Problem
  A commutative generalization of the gauge symmetry group is proposed. The
two-parametric family of two-connected abelian Lie groups is obtained. The
necessity of existence of so-called imaginary charges and electromagnetic
fields with negative energy density (dark photons) is derived. The
possibilities when the overall Lagrangian represents a sum or difference of two
identical Lagrangians for the visible and hidden sectors (i.e. copies of
unbroken) are ruled out by the extended symmetry. The distinction between the
two types of fields resides in the fact that for one of them current and
electromagnetic kinetic terms in Lagrangians are identical in sign, whereas for
another type these terms are opposite in sign. As a consequence, and in
contrast to the common case, like imaginary charges attract and unlike charges
repel. Some cosmological issues of the proposed hypothesis are discussed.
Particles carrying imaginary charges ("allotons") are proposed as dark matter
candidates. Such a matter would be imaginary charged on a large scale for the
reason that dark atoms would carry non-compensated charges. Consequently, there
exist (dark) electromagnetic fields with negative energy density on
cosmological scales (the reviving of the idea of Faradayan cosmology). This
leads to the hypothesis that the modern state of the Universe is
radiation-dominated by dark photons with negative energy density that is the
source of the observed late-time cosmological acceleration. This provides an
explanation for the small value of the cosmological constant as a renormalized
vacuum energy.
