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

In this work we determine the correspondence between quintessence and tachyon dark energy models with a constant dark energy equation of state parameter, we. 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 explicitly demonstrate that if we≠−1 the potentials need to be very fine-tuned for the relative perturbation on the equation of state parameter, Δwe/(1+we)≪1, to be very small around the present time. We also discuss possible implications of our results for the reconstruction of the evolution of we with redshift using varying couplings.