Doug,
I wrote the paragraphs following this one on my blog site. I read your essay quite some time ago and scored it. I remember being favorably disposed to your paper, but I don't remember what I gave it. I was going to write something about whether this idea of a path integral is a Euclideanized form and is then really a sort of neural network "Boltzmann machine" idea. However, I never got back to writing about this. I have been rather occupied in the last month or so.
The solution a ~ t^{1/2} is the matter dominated result and t^{2/3} is the radiation dominated result. If you have
da/dt = a*const*sqrt(ρ)
then for a ~ t^n, then for ρ ~ a^{-3} matter density you have
t^{n-1} ~ t^n t^{-3n/2}
this means that n -1 = -3n/2 + n === > n = 2/3, and for ρ ~ a^4 for radiation, this gives n - 1 = -2n, so n = 1/2. This is a fairly standard result. I did write e^{3t/2} and I really meant t^{2/3} and t^{1/2}. This is a rather curious mistake, and I am not sure why I wrote this. This appears to be a rather embarrassing brain fart.
Your comments about interactions and entanglements are interesting. It is a bit late for me to go into this, so I will do so tomorrow. There is something odd occurring with entanglement is that the gravity field is not local in the way other fields are. The nonlocality of gravity, or really quantum gravity, changes the nature of entanglement. Most QFTs are local, such as the Wightman canonical quantization condition and causality one gets in basic QFT texts. Gravitation is different, and I think entanglement monogamy and such may no longer apply.
Cheers LC
