Scheme dependence of quantum gravity on de Sitter background
  We extend our investigation of the IR effects on the local dynamics of matter
fields in quantum gravity. Specifically we clarify how the IR effects depend on
the change of the quantization scheme: different parametrization of the metric
and the matter field redefinition. Conformal invariance implies effective
Lorentz invariance of the matter system in de Sitter space. An arbitrary choice
of the parametrization of the metric and the matter field redefinition does not
preserve the effective Lorentz invariance of the local dynamics. As for the
effect of different parametrization of the metric alone, the effective Lorentz
symmetry breaking term can be eliminated by shifting the background metric. In
contrast, we cannot compensate the matter field redefinition dependence by such
a way. The effective Lorentz invariance can be retained only when we adopt the
specific matter field redefinitions where all dimensionless couplings become
scale invariant at the classical level. This scheme is also singled out by
unitarity as the kinetic terms are canonically normalized.
