Adiabatic invariant approach on Friedmann cyclic universe

TL;DR

This paper applies the adiabatic invariant approach to a Friedmann closed universe model, deriving the world period and comparing it with classical Friedmann calculations, thus providing new insights into cyclic cosmology.

Contribution

It introduces the adiabatic invariant method combined with Noether gauge symmetry to analyze cyclic universe models, offering a novel analytical perspective.

Findings

World period estimated at ~15.8 Gy, consistent with Friedmann's formula.

Revisits cosmological force and derives Lagrangian density from Rosen's concepts.

Demonstrates the effectiveness of adiabatic invariants in cyclic universe analysis.

Abstract

Oscillating or cyclic models of the universe were inspired by Friedmann's seminal paper of 1922. The model supposes a closed universe. In this work, we study Friedmann closed universe using the adiabatic invariant approach. We start revisiting the cosmological force proposed by N. Rosen and derive the Lagrangian density from Rosen's concepts of cosmological force. Importantly, we introduce the Noether gauge symmetry followed by the Rund-Traumann identity (RTI) and adiabatic invariant approach to examine the cyclic models. We consider a single component form of relativistic matter (stiff matter) at $a(t=0)$ and $a(t=T)$, and surprisingly discover the world period is given by $\sim 15.8$ Gy which is very close to that computed using the Friedmann's formula for the cyclic universe.