Of pNGB QuiNtessence

Abstract

We review the pNGB quintessence models, and point out that the reason why the large decay constants $f_a \ga {\cal O}(1)M_{Pl}$ are really needed is to tame a tachyonic instability present for a wide range of initial $vev$s. Starting very close to potential maxima does not help because quantum fluctuations during early inflation at a scale $H_I$ 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 $f_a > M_{Pl}$ 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 {\it together} even if all of their decay constants obey $f_a < M_{Pl}$. Starting with their $vev \sim f_a$, the pNGBs will hold each other up on the potential for a longer time period. Their effective dynamics is captured by a collective mode, containing admixtures of all of the rolling pNGBs, which behaves as an ultralight field with $f_{eff} > M_{Pl}$. We point out that there may be potentially observable large scale disturbances in the sea of dark energy in such models.