Pre-big bang collapsing universe from modern Kaluza-Klein theory of gravity

TL;DR

This paper explores a collapsing universe model derived from 5D Kaluza-Klein gravity, revealing a finite, vacuum-dominated asymptotic universe with specific back-reaction effects and no singularities.

Contribution

It introduces a novel 5D Kaluza-Klein framework for universe collapse, demonstrating a finite, nonsingular asymptotic state with unique back-reaction characteristics.

Findings

Asymptotic universe is finite in size and energy density.

Back-reaction effects are given by a negative constant.

Universe exhibits vacuum-dominated equation of state.

Abstract

We study the collapse of the universe described by a scalar field spherically symmetric collapse of a system described by a massless scalar field from a 5D Riemann-flat canonical metric, on which we make a dynamical foliation on the extra space-like dimension. The asymptotic universe (absent of singularities) results to be finite in size and energy density, with an vacuum dominated equation of state. The important result here obtained is that the asymptotic back-reaction effects are given by a negative constant: $1/2 [\frac{1}{1+\dot\psi^2}+\frac{1}{\dot\psi^2}] <(\dot{\delta\bar{\phi}})^2>+{1\over 2a^2} <(\vec{\nabla}\delta\phi)^2>|_{t\rightarrow\infty} = {-8 \Lambda_0 \over 3 \pi G}$.