  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.
