Inflaton and metric fluctuations in the early universe from a 5D vacuum state

TL;DR

This paper extends a formalism to analyze gauge-invariant metric fluctuations in the early universe within a 5D vacuum framework, revealing their reciprocal evolution and spectral properties.

Contribution

It introduces a complete formalism for studying metric and inflaton fluctuations in a 5D vacuum, linking their evolution and spectral index.

Findings

The spectral index of fluctuations is between 0.9483 and 1.

Metric and inflaton fluctuations are reciprocally related.

The formalism incorporates a noncompact Kaluza-Klein approach.

Abstract

In this letter we complete a previously introduced formalism to study the gauge-invariant metric fluctuations from a noncompact Kaluza-Klein theory of gravity, to study the evolution of the early universe. The evolution of both, metric and inflaton field fluctuations are reciprocally related. We obtain that <\delta\rho/\rho_b$ depends on the coupling of $\Phi$ with $\delta\phi$ and the spectral index of its spectrum is: $0.9483 < n_1 < 1$.