There's a new paper by Barbour on Arvix, "Entropy and the Typicality of Universes". It's not about an oscillatory model, but, per remarks that include note 18 on its p.10, it puts the transition from an expanding to a contracting phase, characteristic of such models, into the spacetime center of a multiverse with dual arrows of time, pointing in opposite directions, and seems to treat entropy as an emergent phenomenon. The math is way beyond me, but the diagrams suggest that the evidence centers around solutions to the three-body problem, which Wikipedia describes as soluble, but only through equations with 10^8,000,000th terms. (The problem was discovered in 1720, through some slight difficulties in figuring the relation between a planet having a satellite and the sun.) Since I'm a procrastinator, I like multiverses without a beginning, but what I'm wondering here is whether any motion superimposed on the spatial expansion or contraction, on either side of the "Janus point" that Barbour uses to designate the boundary between the forward and backward flows of time, might've resulted in the quantum perturbations that cosmologists everywhere seem to take for granted. If it hasn't, any other explanation for them would be welcome.