Quintessence and tachyon dark energy models with a constant equation of state parameter

TL;DR

This paper explores the relationship between quintessence and tachyon dark energy models with a constant equation of state, revealing differences in scalar field evolution and the fine-tuning needed for potentials when $w_e eq -1$.

Contribution

It demonstrates that despite similar Hubble parameter evolution, quintessence and tachyon models differ in scalar field behavior and highlights the fine-tuning required for potentials with $w_e eq -1$.

Findings

Scalar field evolution differs between models despite similar Hubble parameters.

Potentials require fine-tuning for $w_e eq -1$ to keep perturbations small.

Implications for reconstructing $w_e$ evolution using varying couplings.

Abstract

In this work we determine the correspondence between quintessence and tachyon dark energy models with a constant dark energy equation of state parameter, $w_e$. Although the evolution of both the Hubble parameter and the scalar field potential with redshift is the same, we show that the evolution of quintessence/tachyon scalar fields with redshift is, in general, very different. We explicity demonstrate that if $w_e \neq -1$ the potentials need to be very fine-tuned for the relative perturbation on the equation of state parameter, $\Delta w_e/(1+w_e) \ll 1$, to be very small around the present time. We also discuss possible implications of our results for the reconstruction of the evolution of $w_e$ with redshift using varying couplings.