Models for little rip dark energy

We examine in more detail specific models which yield a little rip cosmology, i.e., a universe in which the dark energy density increases without bound but the universe never reaches a finite time singularity. We derive the conditions for the little rip in terms of the inertial force in the expanding universe and present two representative models to illustrate in more detail the difference between little rip models and those which are asymptotically de Sitter. We derive conditions on the equation of state parameter of the dark energy to distinguish between the two types of models. We show that coupling between dark matter and dark energy with a little rip equation of state can alter the evolution, changing the little rip into an asymptotic de Sitter expansion. We give conditions on minimally coupled phantom scalar field models and on scalar-tensor models that indicate whether or not they correspond to a little rip expansion. We show that, counterintuitively, despite local instability, a little rip cosmology has an infinite lifetime.