I didn't like that paper, as its far fetched and going on about a nonissue imo.
Actually, I really don't understand the conceptual problem in the first place or why people are still harping about the arrow of time and what it can possibly solve. As far as I can see, this has been settled for nearly a hundred years and the answer was given by the second law - period! This is the unique arrow of time and we aren't reversible.
We observe the universe now (call it Z2) and to the time of last scattering (call it Z1), and we see that the entropy of Z2 is a little higher than Z1. Nothing unusual there, we'd obviously have a major problem if it was upside down. In the future at some time (call it Z3), we'd expect the entropy to be even higher. Good!
People wonder why Z1 is small relative to what it could be (we'll call that Zavg, where Zavg is the entropy of a random universe in some thermalized and highly likely state in the ensemble of possible universe wide configurations) and as far as I can see, the best answer is, it is the way it is by observation (somewhat begging the question granted).
Recently with the multiverse craze, people like to try to make everything a density fluctuation and wonder why we aren't a Boltzman brain instead. Well, again, we probably could have been, but observation again rules that out and falsifies the hypothesis. So we're back to square one. Z1 is simply an initial condition that breaks the symmetry.
If there is, for instance, a Hartle-Hawking wavefunction, then this makes perfectly good sense. A single initial state has entropy ~ln(1) = 0.