Big Rip in SO(1,1) phantom universe

TL;DR

This paper investigates the occurrence of the Big Rip in an SO(1,1) phantom universe model with inverse linear potential, analyzing late-time behavior, symmetries, and the role of the SO(1,1) charge.

Contribution

It introduces the SO(1,1) phantom universe model with inverse linear potential and explores its late-time dynamics and symmetry properties related to the Big Rip scenario.

Findings

The universe experiences a Big Rip with the field approaching zero.

The phantom equation of state reaches a late-time minimum of w=-3.

Symmetries T and CT are significant in the universe's final state.

Abstract

For the inverse linear potential, the SO(1,1) field behaves as phantom for late time and the Big Rip will occur. The field approaches zero as time approaches the Big Rip, here. For this potential the phantom equation of state takes the late-time minimum $w_\Phi=-3$. We give some discussions that the Big Rip in the SO(1,1) model may be treated as either the transition point of universe from expansion to extract phase or the final state. In the latter picture of the universe, the field has the $T$ symmetry and the scale factor possesses the $CT$ symmetry, for which the SO(1,1) charge $\bar{Q}$ plays a crucial role.