5D Generalized Inflationary Cosmology

TL;DR

This paper explores a 5D cosmological model with a generalized time coordinate, analyzing different matter eras, phase transitions, and their effects on universe expansion, showing asymptotic convergence to standard 4D models in certain cases.

Contribution

It introduces a 5D inflationary cosmological scenario with phase transitions between matter eras, extending standard models and analyzing their thermodynamic and geometric properties.

Findings

Phase transition affects expansion rate minimally.

Open and closed universes tend to standard 4D models asymptotically.

Flat universe does not approach a standard 4D limit.

Abstract

We consider 5D Kaluza-Klein type cosmological model with the fifth coordinate being a generalization of the invariant ``historical'' time $\tau $ of the covariant theory of Horwitz and Piron. We distinguish between vacuum-, off-shell matter-, and on-shell matter-dominated eras as the solutions of the corresponding 5D gravitational field equations, and build an inflationary scenario according to which passage from the off-shell matter-dominated era to the on-shell one occurs, probably as a phase transition. We study the effect of this phase transition on the expansion rate in both cases of local $O(4,1)$ and $O(3,2)$ invariance of the extended $(x^\mu ,\tau )$ manifold and show that it does not change in either case. The expansion of the model we consider is not adiabatic; the thermodynamic entropy is a growing function of cosmic time for the closed universe, and can be a growing function of historical time for the open and the flat universe. A complete solution of the 5D gravitational field equations is obtained for the on-shell matter-dominated universe. The open and the closed universe are shown to tend asymptotically to the standard 4D cosmological models, in contrast to the flat universe which does not have the corresponding limit. Finally, possible cosmological implications are briefly discussed.