  If we assume that the cosmic energy density will remain constant or strictly
increase in the future, then the possible fates for the universe can be divided
into four categories based on the time asymptotics of the Hubble parameter
H(t): the cosmological constant, for which H(t) = constant, the big rip, for
which H(t) goes to infinity at finite time, the little rip, for which H(t) goes
to infinity as time goes to infinity, and the pseudo-rip, for which H(t) goes
to a constant as time goes to infinity. Here we examine the last of these
possibilities in more detail. We provide models that exemplify the pseudo-rip,
which is an intermediate case between the cosmological constant and the little
rip. Structure disintegration in the pseudo-rip depends on the model
parameters. We show that pseudo-rip models for which the density and Hubble
parameter increase monotonically can produce an inertial force which does not
increase monotonically, but instead peaks at a particular future time and then
decreases.
