Dynamics of tachyon field with an inverse square potential in loop quantum cosmology

TL;DR

This paper studies the behavior of tachyon fields with an inverse square potential within loop quantum cosmology, analyzing stability and late-time power-law expansion, and exploring implications for dark matter and dark energy.

Contribution

It introduces a dynamical system approach to tachyon fields in loop quantum cosmology, identifying stable solutions and their cosmological significance.

Findings

Late-time power-law expansion driven by tachyon field.

Existence of up to five fixed points with two stable attractors.

Potential for tachyon field to model dark matter and dark energy.

Abstract

The dynamical behavior of tachyon field with an inverse potential is investigated in loop quantum cosmology. It reveals that the late time behavior of tachyon field with this potential leads to a power-law expansion. In addition, an additional barotropic perfect fluid with the adiabatic index $0<\gamma<2$ is added, and the dynamical system is shown to be an autonomous one. The stability of this autonomous system is discussed using phase plane analysis. There exist up to five fixed points with only two of them possibly stable. The two stable node (attractor) solutions are specified, and their cosmological indications are discussed. For the tachyon dominated solution, the further discussion is stretched to the possibility of considering tachyon field as a combination of two parts which respectively behave like dark matter and dark energy.