A solution to the problem posed by Byland and Scialom

TL;DR

This paper addresses a stability analysis problem in cosmological dynamical systems, providing a solution to determine the stability of a degenerate critical point and discussing the asymptotic behavior near another critical point.

Contribution

It offers a novel method to analyze the stability of degenerate critical points in Bianchi and Kantowski-Sachs universe models.

Findings

The degenerate critical point is unstable both in the past and future.

The asymptotic behavior near another critical point is characterized.

A solution to a previously posed stability problem is provided.

Abstract

Recently, Byland and Scialom studied the evolution of the Bianchi I, the Bianchi III and the Kantowski-Sachs universe on the basis of dynamical systems methods (Phys. Rev. D57, 6065 (1998), gr-qc/9802043). In particular, they have pointed out a problem to determine the stability properties of one of the degenerate critical points of the corresponding dynamical system. Here we give a solution, showing that this point is unstable both to the past and to the future. We also discuss the asymptotic behavior of the trajectories in the vicinity of another critical point.