Dynamics of phantom model with O(N) symmetry in loop quantum cosmology

TL;DR

This paper explores the dynamics of a phantom field with O(N) symmetry within loop quantum cosmology, revealing saddle point stability and contrasting behaviors with general relativity, highlighting the influence of symmetry on cosmic evolution.

Contribution

It provides a detailed phase-space analysis of the O(N) symmetric phantom model in LQC, showing the impact of symmetry on stability and evolution, differing from classical GR results.

Findings

No stable nodes, only saddle points in phase space.

O(N) symmetry affects the universe's evolution details.

Dynamics resemble single-field phantom models in LQC.

Abstract

Many astrophysical data show that the expansion of our universe is accelerating. In this paper, we study the model of phantom with O(N) symmetry in background of loop quantum cosmology(LQC). We investigate the phase-space stability of the corresponding autonomous system and find no stable node but only 2 saddle points in the field of real numbers. The dynamics is similar to the single-field phantom model in LQC[1]. The effect of O(N) symmetry just influence the detail of the universe's evolution. This is a sharp contrast with the result in general relativity, in which the dynamics of scalar fields models with O$(N)$ symmetry are quite different from the single-field models[2][3][4].