  We extend our investigation of soft graviton effects on the microscopic
dynamics of matter fields in de Sitter space. We evaluate the quantum equation
of motion in generic gauge theories. We find that the Lorentz invariance can be
respected and the velocity of light is not renormalized at the one-loop level.
The gauge coupling constant is universally screened by soft gravitons and
diminishes with time. These features are in common with other four dimensional
field theories with dimensionless couplings. In particular the couplings scale
with time with definite scaling exponents. Although individual scaling
exponents are gauge dependent, we argue that the relative scaling exponents are
gauge independent and should be observable. We also mention soft graviton
effects on cosmic microwave background.
