Abstract
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.
Highlights
There is overwhelming evidence for a recent acceleration of the expansion of the universe [1, 2]
At present the observational data appears to be consistent with a constant dark energy density, known as a cosmological constant, with a constant dark energy equation of state parameter, we = −1
Dynamical dark energy candidates include minimally coupled scalar fields, vector fields or even modifications to General Relativity on cosmological scales [3, 4], such as those associated with extra-dimensions [5,6,7] or f (R) theories [8,9,10,11]
Summary
There is overwhelming evidence for a recent acceleration of the expansion of the universe [1, 2]. At present the observational data appears to be consistent with a constant dark energy density, known as a cosmological constant, with a constant dark energy equation of state parameter, we = −1. Current observations seem to be consistent with a constant we = −1, it is interesting to ask how likely it is for the dark energy parameter to be a constant other than −1 This question has been addressed in [12] where it has been shown that a considerable amount of fine-tuning of the quintessence scalar field potential would be required in order to obtain a constant we = −1.
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