Tracking Quintessence Would Require Two Cosmic Coincidences

Abstract

Good tracking requires that the quintessence energy fraction slowly increase while the roll $λ\equiv -d\ln V/\varkappa dϕ$ slowly decreases, but is not yet truly slow-rolling. The supernova bound on the present quintessence equation of state requires either (1) a cosmological constant or other fine-tuned "crawling quintessence" or (2) "roll-over quintessence" that tracked until recently, but now became slow rolling, because of a sharp increase in potential curvature. Thus, fine-tuning is required by constant equation of state and inverse power potentials, but can be avoided by the SUGRA and Skordis-Albrecht potentials and other good trackers, provided quintessence energy domination and slow roll {\em both} began only recently. This makes the time in which we live special in {\em two} respects.