Any unified early and late dark energy scenario with a single tracking scalar field requires a potential with three distinct slopes arranged in a steep-steeper-shallow hierarchy.
Phenomenological parameterization of quintessence
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We propose a simple phenomenological parameterization of quintessence with a time-varying equation of state. In particular, it accounts for the possibility of early dark energy. The quintessence potential can be reconstructed in terms of the present fraction in dark energy, the present equation of state and the amount of early dark energy.
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Unifying Early and Late Dark Energy: Dynamical Requirements and Obstructions
Any unified early and late dark energy scenario with a single tracking scalar field requires a potential with three distinct slopes arranged in a steep-steeper-shallow hierarchy.