Primordial SdS universe from a 5D vacuum: scalar field fluctuations on
  Schwarzschild and Hubble horizons
  We study scalar field fluctuations of the inflaton field in an early
inflationary universe on an effective 4D Schwarzschild-de Sitter (SdS) metric,
which is obtained after make a planar coordinate transformation on a 5D
Ricci-flat Schwarzschild-de Sitter (SdS) static metric. We obtain the important
result that the spectrum of fluctuations at zeroth order is independent of the
scalar field mass $M$ on Schwarzschild scales, while on cosmological scales it
exhibits a mass dependence. However, in the first-order expansion, the spectrum
depends of the inflaton mass and the amplitude is linear with the Black-Hole
(BH) mass $m$.
