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We review the pNGB quintessence models, and point out that the reason why the large decay constants fₐ O (1) M₋ are really needed is to tame a tachyonic instability present for a wide range of initial vevs. Starting very close to potential maxima does not help because quantum fluctuations during early inflation at a scale HI perturb the quintessence vev, displacing it from the maxima. This issue is quite interesting for pNGB dark energy in light of the recently discussed difficulties with embedding models with fₐ > M₋ in fundamental theory. A possible way around is provided by models with several ultralight pNGBs, which can drive a short burst of very late inflation together even if all of their decay constants obey fₐ M₋. We point out that there may be potentially observable large scale disturbances in the sea of dark energy in such models.
Kaloper et al. (Wed,) studied this question.