Soft gravitational effects in Kadanoff-Baym approach
  In de Sitter space, the gravitational fluctuation at the super-horizon scale
may make physical quantities time dependent by breaking the de Sitter symmetry.
We adopt the Kadanoff-Baym approach to evaluate soft gravitational effects in a
matter system at the sub-horizon scale. This investigation proves that only the
local terms contribute to the de Sitter symmetry breaking at the one-loop
level. The IR singularities in the non-local terms cancel after summing over
degenerate states between real and virtual processes. The corresponding IR
cut-off is given by the energy resolution like QED. Since the energy resolution
is physical and independent of cosmic evolution, the non-local contributions do
not induce the de Sitter symmetry breaking. We can confirm that soft
gravitational effects preserve the effective Lorentz invariance.
