Horizons and distance

A while ago I posed a question in the paper journal. I will repeat it here.

In many cosmological models we have the length scale parameter R. This is the dynamical object which describes a fiducial scale (often set to 1 in our current epoch). It is described by solutions to the Einstein equations for a homogeneous isotropic universe. In most cosmological discussions we also have the radius of the particle horizon. How do their evolutions compare as time decreases approaching zero?

What I am thinking about here are reasons for a low entropic beginning. If (moving backward in time) two arbitrary points become acausal (outside each others particle horizons) than space becomes disconnected. What does this mean? Most geometrical theories require that a space provide compact support and be generally well behaved. This is true, for example, when one computes the spherical entropy bount of the Holographic principle. What is the entropy of a completely causally disconnected space? Would this mean that the initial singularity has a different form?
I see elements of this question when I read articles about the holographic principle.Banks and Fischler describe the natural arrow of time resulting from their Holographic Cosmology 3.0:

Time evolution (as seen by a given observer) is constrained in such a way that at early times, only degrees of freedom which are wthin the particle horizon, are correlated by the dynamics.

I guess they are describing colliding paritcle horizons. What happens in the reverse?
As far as I have been taught, both time and space collapse to a singularity where they are both zero. Thus it would seem that the horizon matches the scale factor. But if R obeys linear superposition then I can add a constant and the initial singularity vanishes. However I think that the Einstein evolution equations for the LFRW universe are not invarient like that. So its not quite that simple but are there coordinate systems where there is no singularity, where the parameter does not pass through zero, ala kruskal coordinates for black holes?

Perhaps there need not be a residual length or time (planck length?) If the length scale is normalized to the horizon and then particle horizon becomes shorter than two points seperated by the length scale are effectively disconnected and if the length scale is always longer than the partical horizon then... all points are disconnected?

Ramble worse than usual today. hm