Metric fluctuations from a NKK theory of gravity in a de Sitter expansion

TL;DR

This paper develops a gauge-invariant formalism for metric fluctuations within a non-compact Kaluza-Klein gravity framework during de Sitter expansion, revealing the influence of the fifth dimension on fluctuation spectra.

Contribution

It introduces a novel gauge-invariant metric fluctuation formalism in NKK gravity and connects the fluctuation spectrum to the fifth dimension, extending standard inflationary results.

Findings

Recovered the standard density fluctuation relation $rac{ riangle ho}{ ho} hickapprox 2\Phi$

Demonstrated the fluctuation spectrum depends on the fifth coordinate

Established an interval of wave numbers linked to the fifth dimension

Abstract

A gauge invariant metric fluctuations formalism from a non-compact Kaluza-Klein (NKK) theory of gravity is presented in this talk notes. In this analysis we recover the well-known result $\frac{delta \rho}{\rho}\simeq 2\Phi$ obtained typically in the standard 4D semiclassical approach to inflation and also the spectrum of this fluctuations becomes dependent of the fifth (space-like) coordinate. This fact allows to establish an interval of values for the wave number associated with the fifth dimension.