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.