We calculate quantum fluctuations of a free scalar field in the Schwarzschild–de Sitter spacetime, adopting the planar coordinates that are pertinent to the presence of a black hole in an inflationary Universe. In a perturbation approach, expanding 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.
Relation:
Classical and Quantum Gravity 28(5), 055004(14pages)
