  This thesis consists of three parts. In the first part we review the
quantization of Yang-Mills theories and perturbative quantum gravity in curved
spacetime. In the second part we calculate the Feynman propagators of the
Faddeev-Popov ghosts for Yang-Mills theories and perturbative quantum gravity
in the covariant gauge. In the third part we investigate the physical
equivalence of covariant Wightman graviton two-point function with the physical
graviton two-point function.
  The Feynman propagators of the Faddeev-Popov ghosts for Yang-Mills theories
and perturbative quantum gravity in the covariant gauge are infrared (IR)
divergent in de Sitter spacetime. We point out, that if we regularize these
divergences by introducing a finite mass and take the zero mass limit at the
end, then the modes responsible for these divergences will not contribute to
loop diagrams in computations of time-ordered products in either Yang-Mills
theories or perturbative quantum gravity. We thus find effective Feynman
propagators for ghosts in Yang-Mills theories and perturbative quantum gravity
by subtracting out these divergent modes.
  It is known that the covariant graviton two-point function in de Sitter
spacetime is infrared divergent for some choices of gauge parameters. On the
other hand it is also known that there are no infrared problems for the
physical graviton two-point function obtained by fixing all gauge degrees of
freedom, in global coordinates. We show that the covariant Wightman graviton
two-point function is equivalent to the physical one in the sense that they
result in the same two-point function of any local gauge-invariant quantity.
Thus any infrared divergence in the Wightman graviton two-point function in de
Sitter spacetime can only be an gauge artefact.
