Abstract
The production of the hypermagnetic gyrotropy is investigated under the assumption that the gauge coupling smoothly evolves during a quasi-de Sitter phase and then flattens out in the radiation epoch by always remaining perturbative. In the plane defined by the strength of the anomalous interactions and by the rate of evolution of the gauge coupling the actual weight of the pseudoscalar interactions turns out to be always rather modest if major deviations from the homogeneity are to be avoided during the inflationary phase. Even if the gauge power spectra are related by duality only in the absence of anomalous contributions, an approximate duality symmetry constrains the late-time form of the hypermagnetic power spectra. Since the hypermagnetic gyrotropy associated with the modes reentering prior to the phase transition must be released into fermions later on, the portions of the parameter space where the obtained baryon asymmetry is close to the observed value are the most relevant for the present ends. For the same range of parameters the magnetic power spectra associated with the modes reentering after symmetry breaking may even be of the order of a few hundredths of a nG over typical length scales comparable with the Mpc prior to the collapse of the protogalaxy.
Highlights
Vainshtein and Zeldovich [4,5] introduced the notion of magnetic gyrotropy by noting that the only possible pseudoscalar quadratic in B must be of the form B · ∇ × B
The purpose of this paper is to address the origin of largescale magnetism and of the baryon asymmetry of the Universe (BAU) in a unified dynamical framework by considering a more general variant of the scenario suggested in Refs. [22,23,24]
We suggest here that the BAU could be the result of the decay of the hypermagnetic gyrotropy
Summary
Vainshtein and Zeldovich [4,5] (see [6,7,8]) introduced the notion of magnetic gyrotropy by noting that the only possible pseudoscalar quadratic in B must be of the form B · ∇ × B. The idea is to produce the hypermagnetic gyrotropy during the quasi-de Sitter stage of expansion while the gauge coupling remains always perturbative This suggestion goes back to the two-step model of Ref. During the quasi-de Sitter stage of expansion the strength of the anomalous interactions (i.e. λ) will turn out to be strongly constrained by the critical density bound but the gyrotropic configurations of the hypermagnetic fields will still be comparable with the values required to seed the BAU. While the SUL (2) anomaly is typically responsible for B and L nonconservation via instantons and sphalerons, the UY (1) anomaly might lead to the transformation of the infrared modes of the hypercharge field into fermions For this reason the production of the BAU demands, in this context, the dynamical generation of the gyrotropic configurations of the hypermagnetic field as argued, in Refs. To avoid extensive digressions some of the technical results that are relevant for the derivations have been relegated to the Appendices A and B
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