Primordial SdS universe from a 5D vacuum: scalar field fluctuations on Schwarzschild and Hubble horizons

TL;DR

This paper investigates scalar field fluctuations in an early universe modeled by a 4D Schwarzschild-de Sitter metric derived from a 5D vacuum, revealing mass-dependent spectra on cosmological scales and a linear relation with black hole mass.

Contribution

It introduces a novel approach to derive a 4D SdS universe from a 5D vacuum and analyzes scalar fluctuations, highlighting their mass dependence on different scales.

Findings

Spectrum at zeroth order is mass-independent on Schwarzschild scales.

On cosmological scales, the spectrum shows mass dependence.

First-order spectrum amplitude is linearly related to black hole mass.

Abstract

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 $m$.