Phantom Field with O(N) Symmetry in Exponential Potential

TL;DR

This paper analyzes the phase space of an O(N) symmetric phantom field with exponential potential, revealing a lower bound on the equation of state for stable attractor solutions and deriving a potential-redshift relation.

Contribution

It introduces the effect of O(N) symmetry on phantom models, establishing a lower bound on the equation of state and deriving a reconstruction relation.

Findings

Lower bound w > -3 for stable attractors

Derived potential-redshift relation

O(N) symmetry affects phase space stability

Abstract

In this paper, we study the phase space of phantom model with O(\emph{N}) symmetry in exponential potential. Different from the model without O(\emph{N}) symmetry, the introduction of the symmetry leads to a lower bound $w>-3$ on the equation of state for the existence of stable phantom dominated attractor phase. The reconstruction relation between the potential of O(\textit{N}) phantom system and red shift has been derived.