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