Evolution of a Large Scale Chern–Simons Magnetic Field in Expanding Space with a Negative Scalar Curvature Parameter

Abstract

We study the problem of breaking non-Abelian gauge symmetry for solving the Yang–Mills equation in an expanding space with a parameter of negative scalar curvature, which becomes flat at large expansion times and which is called the geodesic flow space of the Lobachevsky plane. We use the following: the physical properties of the magnetic field are related to the Kolmogorov scale, which made it possible to estimate the α-effect of the space curvature parameter at each moment of time. On the other hand, in an expanding hyperbolic space, a change in the density of magnetic helicity is observed, unrelated to the α-effect. We compare the two indicated factors of change in magnetic helicity and conclude that, at a fairly stable stage of expansion, the α-effect caused by the influence of scalar curvature on the Kolmogorov MHD spectrum becomes small.