Distinguishing Marks of Simply-connected Universes

TL;DR

The paper introduces a statistical method to distinguish simply-connected Robertson-Walker universes, providing explicit formulas and graphical analysis, and improves techniques for identifying topological signatures of multiply-connected universes.

Contribution

It presents a new statistical quantity for identifying simply-connected RW universes and refines methods for detecting topological signatures in multiply-connected universes.

Findings

Explicit expressions for the distinguishing statistic for all simply-connected RW classes.

Graphs illustrating the distinguishing marks for each universe class.

Enhanced procedures for topological signature extraction in cosmological models.

Abstract

A statistical quantity suitable for distinguishing simply-connected Robertson-Walker (RW) universes is introduced, and its explicit expressions for the three possible classes of simply-connected RW universes with an uniform distribution of matter are determined. Graphs of the distinguishing mark for each class of RW universes are presented and analyzed.There sprout from our results an improvement on the procedure to extract the topological signature of multiply-connected RW universes, and a refined understanding of that topological signature of these universes studied in previous works.