Generalization of Abelian Gauge Symmetry and the Dark Matter and Energy Problem

Abstract: 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.