I know this is dumb, but I'm just not getting any sort of intuition for what the "comoving Hubble radius" is. I have the definition in front of me in a book which says that it is equal to (in c = 1 units): (aH)-1 With a being the scale factor and H the Hubble parameter. So basically, it must be equal to dt/da. Later on, there is a statement that it is the "distance over which particles can travel in the course of one expansion time i.e. roughly the time in which the scale factor doubles." I'm not seeing how that follows from the definition. Later still, the book states: "...if [particles] are separated by distances larger than the Hubble radius, then they cannot currently communicate." I'm not seeing how this statement follows from the previous one. I'm not sure if I even understand what "currently communicate" means since communication can't happen instantaneously anyway. The book is careful to make a distinction between this and the comoving horizon scale, which I understand perfectly well. If particles are separated by a comoving distance greater than the comoving horizon scale, then they could never have communicated in the history of the universe, since it represents the largest distance over which information can have propagated at any time.