On the exact solutions of the Bianchi IX cosmological model in the proper time

TL;DR

This paper investigates the potential for an exact four-parameter analytic solution to the Bianchi IX cosmological model in proper time, using the Painlevé test to explore its integrability and possible extensions.

Contribution

It provides a perturbative analysis confirming the potential existence of a four-parameter extension to known solutions of the Bianchi IX model.

Findings

Painlevé test suggests integrability of the model in proper time.

Possible existence of a four-parameter analytic solution is supported.

Extension beyond the known three-parameter solution is plausible.

Abstract

It has recently been argued that there might exist a four-parameter analytic solution to the Bianchi IX cosmological model, which would extend the three-parameter solution of Belinskii et al. to one more arbitrary constant. We perform the perturbative Painlev\'e test in the proper time variable, and confirm the possible existence of such an extension.