Euclidean 5-sphere archaic universe

TL;DR

This paper explores a cosmological model based on Euclidean 5-sphere geometry, proposing a pre-cosmic phase and a nucleation process for the big bang, with a complete solution to Projective General Relativity equations.

Contribution

It introduces a novel pre-cosmic evolution parameter and provides a complete solution to PGR equations within this framework, linking geometry and physics of the archaic universe.

Findings

Proposes a quantum precursor to physical time as an evolution parameter.

Provides a complete solution to PGR equations in the De Sitter universe.

Establishes relations between scale factor and cosmic time in the model.

Abstract

In this work, we examine in depth the cosmological physical aspects of the archaic universe described by Euclidean 5-sphere geometry. (see Int. Jour. of Theor., Phys 2009, 48:1003-1018). We hypothesize that the big bang consisted of a spatially extended nucleation process which took place at the end of a pre-cosmic phase, characterized by the evolution parameter x0. This parameter, which can be considered a quantum precursor of ordinary physical time, is a coordinate of Euclidean 5-sphere metrics. We must now examine what the privileged role of the x0 axis consists in. The big bang is a sort of nucleation of matter and fields by vacuum; to try to understand it we must therefore make some assumptions regarding a pre-cosmic state of matter and energy. The introduction of an evolution parameter such as x0 which can be extended to pre-big bang situations is absolutely necessary if we are to define any pre-cosmic dynamics. A generalized Bekenstein relation is here proposed for archaic Universe. A complete solution to Projective General Relativity (PGR) equations in the De Sitter Universe is provided, so as to establish univocal relations between the scale factor R(tau) and cosmic time tau. In this way, the physics and geometry of the cosmological model are specified completely.