The effects of the U$_\textrm{Y}$(1) Chern-Simons term and its baryonic contribution on matter asymmetries and hypermagnetic fields

TL;DR

This paper investigates how the U_Y(1) Chern-Simons term and its baryonic contribution influence the evolution of matter asymmetries and hypermagnetic fields in the early universe, revealing conditions for their growth and saturation.

Contribution

It demonstrates the impact of the Chern-Simons term and baryonic effects on matter asymmetry and hypermagnetic field evolution, including saturation phenomena and implications for cosmological data.

Findings

Initial hypermagnetic fields can generate matter asymmetries.

Baryonic contributions lower the saturation threshold.

Results align with current observational constraints when inverse cascade is considered.

Abstract

In this paper, we study the significance of the U$_\textrm{Y}$(1) Chern-Simons term in general, and its baryonic contribution in particular, for the evolution of the matter asymmetries and the hypermagnetic field in the temperature range $100$GeV$\leq T \leq 10$TeV. We show that an initial helical hypermagnetic field, denoted by $B_Y^{(0)}$, can grow matter asymmetries from zero initial value. However, the growth which is initially quadratic with respect to $B_Y^{(0)}$, saturates for values larger than a critical value. The inclusion of the baryonic contribution reduces this critical value, leading to smaller final matter asymmetries. Meanwhile, $B_Y(T_{EW})$ becomes slightly larger than $B_Y^{(0)}$. In the absence of the U$_\textrm{Y}$(1) Chern-Simons term, the final values of matter asymmetries grow without saturation. Conversely, we show that an initial matter asymmetry can grow an initial seed of hypermagnetic field, provided the Chern-Simons term is taken into account. The growth process saturates when the matter asymmetry drops abruptly. When the baryonic contribution is included, the saturation occurs at an earlier time, and $B_Y (T_{EW})$ becomes larger. We also show the results can be within the acceptable range of present day data, provided the inverse cascade process is also taken into account.