Point splitting renormalization of Schwinger induced current in de   Sitter spacetime
  The covariant and gauge invariant calculation of the current expectation value in the homogeneous electric field in 1+3 dimensional de Sitter spacetime is shown. The result accords with previous work obtained by using adiabatic subtraction scheme. We therefore conclude the counterintuitive behaviors of the current in the infrared (IR) regime such as IR hyperconductivity and negative current are not artifacts of the renormalization scheme, but are real IR effects of the spacetime. 
Takahiro Hayashinaka, Jun'ichi Yokoyama
hep-th astro-ph.CO gr-qc