Scalar field fluctuations in Schwarzschild-de Sitter space-time
Hing-Tong Cho, Kin-Wang Ng, I-Chin Wang
TL;DR
This paper investigates quantum fluctuations of a scalar field in Schwarzschild-de Sitter space-time, focusing on the effects of a small black hole in an inflationary universe and deriving the scalar power spectrum.
Contribution
It introduces a perturbative method to analyze scalar field fluctuations in Schwarzschild-de Sitter space-time with a small black hole, providing new insights into their evolution and spectrum.
Findings
Derived the time evolution of quantum fluctuations.
Obtained the scalar power spectrum in the presence of a black hole.
Showed the impact of black hole size on fluctuation behavior.
Abstract
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.
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