New perspectives on future rip scenarios with holographic dark energy

We explore the asymptotic future evolution of holographic dark energy (HDE) models, in which the density of the dark energy is a function of a cutoff scale $L$. We develop a general methodology to determine which models correspond to future big rip, little rip, and pseudo-rip (de Sitter) evolution, and we apply this methodology to a variety of well-studied HDE models. None of these HDE models display little rip evolution, and we are able to show, under very general assumptions, that HDE models with a Granda-Oliveros cutoff almost never evolve toward a future little rip. We extend these results to HDE models with nonstandard Friedman equations and show that a similar conclusion applies: little rip evolution is a very special case that is almost never realized in such models.