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Abstract
A commutative generalization of the U(1) 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 U(1)) 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 are proposed as one of the components of dark matter. Such a matter would be imaginarily charged on a large scale for the reason that dark atoms carry non-compensated charges. It leads to important predictions for matter distribution, interaction and other physical properties being different from what is observed in dominant dark matter component in the standard model. These effects of imaginary charges depend on their density and could be distinguished in future observations. Dark electromagnetic fields can play crucial dynamical role in the very early universe as they may dominate in the past and violate weak energy condition which provides physical grounds for bouncing cosmological scenarios pouring a light on the problem of origin of the expanding matter flow.
Highlights
The idea of interactions (even long-range U (1) interactions) in the dark sector is not new [1]
The authors point out that the dark photon comes from gauge symmetry, just like the ordinary photon, and its masslessness is completely natural
Whereas the Lagrangian (15) may be schematically presented as L1 = Lmat − F 2 + Lm′ at + f 2, the expression (19) is of the form L2 = Lmat − F 2 − Lm′ at − f 2
Summary
The idea of interactions (even long-range U (1) interactions) in the dark sector is not new [1]. A novel symmetry of the action is the symmetry under the transformation mixing the fields Φ ( x) ↔ Ψ ( x) , gμν ( x) ↔ gαβ ( x) and under the subsequent change of the overall sign, S → −S Linde calls this the antipodal symmetry, since it relates to each other the states with positive and negative energies. O (2) , which is non-commutative even in the case of two dimensions This is inconsistent with our attempt to derive the existence of minus-fields analogically to electromagnetic ones, i.e. from a commutative group of lagrangian symmetries. In order to bring about invariance of the Lagrangian (15) up to change of sign, transformations sα must be accompanied by mixing of the fields φ and ψ. The overall sign of the Lagrangian (15) changes
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