Schwinger Effect by an $SU(2)$ Gauge Field during Inflation

TL;DR

This paper investigates the Schwinger effect in an $SU(2)$ gauge field during inflation, revealing suppression of pair production compared to $U(1)$ due to isotropic vacuum effects, and concludes it doesn't threaten inflationary dynamics.

Contribution

It provides the first detailed analysis of the Schwinger effect in a non-Abelian $SU(2)$ gauge field during inflation, highlighting differences from the Abelian case and implications for inflation models.

Findings

Schwinger pair production decreases with increasing interaction strength in $SU(2)$.

The effective mass of scalar fields is greater in $SU(2)$ due to isotropic vacuum expectation values.

The Schwinger effect is negligible in weak interaction regimes, not affecting inflationary dynamics.

Abstract

Non-Abelian gauge fields may exist during inflation. We study the Schwinger effect by an $SU(2)$ gauge field coupled to a charged scalar doublet in a (quasi) de Sitter background and the possible backreaction of the generated charged particles on the homogeneous dynamics. Contrary to the Abelian $U(1)$ case, we find that both the Schwinger pair production and the induced current decrease as the interaction strength increases. The reason for this suppression is the isotropic vacuum expectation value of the $SU(2)$ field which generates a (three times) greater effective mass for the scalar field than the $U(1)$. In the weak interaction limit, the above effect is negligible and both the $SU(2)$ and $U(1)$ cases exhibit a linear increase of the current and a constant conductivity with the interaction strength. We conclude that the Schwinger effect does not pose a threat to the dynamics of inflationary models involving an $SU(2)$ gauge field.