Phantom evolution in power-law potentials

TL;DR

This paper analyzes phantom dark energy models with power-law potentials, deriving early-time tracker solutions and comparing analytical approximations with numerical results, revealing bounds on potential exponents and high accuracy in cosmological evolution predictions.

Contribution

It provides analytical solutions for phantom models with power-law potentials and establishes bounds on potential exponents, enhancing understanding of their cosmological behavior.

Findings

Energy positivity requires normal power-law potentials.

Tracker solutions match numerical results within 2% for z>1.5.

Intermediate solutions are accurate within 2% up to z≈0.5.

Abstract

We investigate phantom models with power-law potentials and we extract the early-time, "tracker", solutions under the assumption of matter domination. Contrary to quintessence case, we find that energy positivity requires normal power-law potentials instead of inverse power-law ones, with the potential exponent being bounded by the quadratic form. In addition, we analytically present the general cosmological solution at intermediate times, that is at low redshifts, which is the period of the transition from matter to dark-energy domination. The comparison with the exact evolution, arising from numerical elaboration, shows that the tracker solution agrees with the later within 2% for redshifts z>1.5, while the intermediate solution is accurate within 2% up to $z\approx 0.5$.