Tracking quintessence and k-essence in a general cosmological background

TL;DR

This paper derives conditions for stable tracker solutions in quintessence and k-essence models within a general cosmological background, identifying key parameters and equations governing their behavior.

Contribution

It provides a comprehensive analysis of stability conditions for tracker solutions in both quintessence and k-essence models in arbitrary cosmological backgrounds.

Findings

Tracker solutions exist only when η is constant.

Explicit expressions for the equation of state are derived.

Enumerates special cases where tracker solutions are possible.

Abstract

We derive conditions for stable tracker solutions for both quintessence and k-essence in a general cosmological background, H^2 \propto f(\rho). We find that tracker solutions are possible only when \eta = d ln f /d ln \rho is constant, aside from a few special cases, which are enumerated. Expressions for the quintessence or k-essence equation of state are derived as a function of \eta and the equation of state of the dominant background component.