Three comoving horizons
(click on image to enlarge)
Comoving horizon sizes, relative to the current Hubble distance dH,o, evaluated for the (2005) concordance model. The Hubble radius is just the distance to superluminal expansion (v = c). The particle horizon is the region size crossed by light since the Big Bang, and is formally equal to c × conformal time; it gives the size of causally connected regions. Note it always gets bigger. The event horizon depends on the future expansion history, and is only finite because we have an accelerating future. As the acceleration picks up speed, the region we will ultimately be able to see shrinks in (comoving) size.
Figure made for this course.