Is the cosmological horizon expanding faster than space itself? I read that the rate of expansion of the universe is still a mystery. But if it's actually decelerating, wouldn't it mean that our cosmological horizon is expanding faster than space, and that one day in the far far future, it will be possible for any two points in the universe to be causally connected?
 A: The particle horizon grows faster than the scale factor (which it has to, because it shows the path of a light ray travelling through space with c, so it has to go farther than a regular comoving galaxy just sitting still on its coordinate in expanding space).
On the space-time-diagrams below the dashed lines are space itself, the dark green line is the particle horizon. Time goes up, space to the side, axes are in Gigayears and Gigalightyears:

As you see in the late universe plot, the particle horizon, being the light cone of t=0, converges to a constant comoving distance (and so does the orange-dashed future light cone of every given time), which means that no, not every part of the universe will once be causaly connected.
The comoving coordinate the particle horizon will converge to is now at a distance of 63.2 Gigalightyears, while the physical distance this rays or neutrinos from the big bang have travelled up to today is 46.4 Gigalightyears. In other words: nothing that is farther away than 63.2 Gyr today will ever be reached by a signal emitted from our coordinate at the big bang.
Here is an alternative depiction of the evolution of the cosmic horizons as shells with 2 space dimensions and an animated time dimension: Link 1, and here a plot for the very late universe: Link 2
