Cosmological horizons in regular bouncing backgrounds

It is often stated that a phase of standard, decelerated cosmological expansion is characterised by the absence of global event horizons, while a phase of accelerated expansion is associated with the absence of particle horizons. This is not necessarily true because such horizons, being non-local properties of the spacetime geometry, depend on the full (past and future) history of the given cosmological background. We provide examples of various different scenarios for the case in which the final asymptotic phase of standard expansion and decreasing curvature is connected, through a regular bounce, with an initial (and possibly infinitely extended in time) regime of growing curvature.