In LQG, the Universe starts off not from a singularity but of finite size. And there may be the idea of a pre-big bang crunch. Assuming the Universe is symmetric in time about the 'big bang'. What would the initial condition be? Presumably as disorder increases with time, the space at the initial condition should be highly ordered. Or the most ordered a spin-network can be. Probably highly symmetrical.
Is there some idea of how to measure the 'disorder' of a spin network?
When thinking of highly ordered networks I can only think of things like $E_8$ lattices and Leech lattices. But that is probably nothing to do with it.
Is the spin-network at the beginning of time even an infinite network?