The w = -1 crossing of the quintom model with slowly-varying potentials

TL;DR

This paper investigates the transition of the equation of state parameter w from above to below -1 in the quintom model with slowly-varying potentials, revealing the dependence on matter density and kinetic energy at the transition.

Contribution

It demonstrates the existence of a w = -1 crossing solution in the quintom model under slow-roll conditions and derives perturbative solutions for the fields.

Findings

Existence of a w = -1 crossing solution in the quintom model.

Transition rate depends on matter density at transition.

Perturbative solutions for the scalar fields are obtained.

Abstract

Considering the quintom model with arbitrary potential, it is shown that there always exists a solution which evolves from w > -1 region to w < -1 region. The problem is restricted to the slowly varying potentials, i.e. the slow-roll approximation. It is seen that the rate of this phase transition only depends on the energy density of matter at transition time, which itself is equal to the kinetic part of quintom energy density at that time. The perturbative solutions of the fields are also obtained.