  We calculate quantum fluctuations of a free scalar field in the
Schwarzschild-de Sitter space-time, adopting the planar coordinates that is
pertinent to the presence of a black hole in an inflationary universe. In a
perturbation approach, doing expansion in powers of a small black hole event
horizon compared to the de Sitter cosmological horizon, we obtain time
evolution of the quantum fluctuations and then derive the scalar power
spectrum.
