Classical transitions with the topological number changing in the early Universe

Abstract

We consider classical dynamics of two real scalar fields within a model with the potential having a saddle point. The solitons of such model are field configurations that have the form of closed loops in the field space. We study the formation and evolution of these solitons, in particular, the conditions at which they could be formed even when the model potential has only one minimum. These non-trivial field configurations represent domain walls in the three-dimensional physical space. The set of these configurations can be split into disjoint equivalence classes. We provide a simple expression for the winding number of an arbitrary closed loop in the field space and discuss the transitions that change the winding number. We also show that non-trivial field configurations could be responsible for the energy density excess that could evade the CMB constraints but could be important at scales which are responsible for the formation of galaxies and the massive primordial black holes.

Multi-kink collisions in the ϕ 6 model

“…For example a two-or three-dimensional domain wall in the direction orthogonal to it can be viewed as a topological soliton (kink) interpolating two different vacua of the model, which are separated by the wall in the two-or three-dimensional world. Besides that, (1+1)-dimensional models can be used as a simplified setup for studying general properties of nonlinear field models [13][14][15][16][17][18][19].…”

Non-topological kink scattering in a two-component scalar field theory model

“…Not only does this magnitude set the final separation velocity but also the nature of the resulting particles. In order to study the evolution of the initial configurations (12) and (13) dictated by the non-linear Klein-Gordon equations (4), numerical analysis will be used. The numerical approach used in this paper follows the algorithm described in [115] by Kassam and Trefethen.…”

“…The characteristics of these solutions have been extensively exploited to explain some non-linear phenomena arising in diverse branches of Physics. To mention just a few examples: signal transmission in optical fibers [1,2,3], the analysis of some features of DNA [4] and other molecular systems [5,6], the description of magnetic flux quanta (fluxons) in Josephson junctions [7,8], the properties of some materials in Condensed Matter [9], the behavior of the Early Universe [10,11,12], etc. Obviously, kinks can move in the physical substrate involved in the previously mentioned applications, so the understanding of the collision processes between these traveling kinks is an essential issue.…”

Multi-kink scattering in the double sine-Gordon model

“…Kinks, domain walls and other topological defects arise in a great amount of models, hence they are very important for various physical applications from condensed matter to high energy physics and cosmology [78][79][80][81][82][83][84][85], see also [2]. Many physical phenomena could be effectively described by one-dimensional topological structures.…”