Since no-one qualified would answer, I'll a give it a shot:

1. Talking quantum mechanics, these bosons have no identity, and their overall state does not even need to have a well-defined particle number in Fock space. This means, mathematically, the cosmic state of e.g. the photon field would be a superposition of one-, two-, three- ... gazillion-photon states, and each of them is symmetrised for particle location. So there is no particle Alice and particle Bob, just amplitudes/probabilities for some interacting in a given space-time volume. Apparently, this state would look like any other with arbitrary density because there is no measure for time and space, once everything is massless bosons.

2. Again, the particle number will be very fuzzy, and maybe very similar to some kind of vacuum with mostly "virtual particles" and such fluctuations (I'm improvising here). I had another question here about entropy. R. Penrose seem to try to get rid of it in evaporating black holes, but I (who am I?) was thinking that it doesn't matter if you have much entropy in microscopic degrees of freedom from the previous aeon that are so uniformely distributed that they don't drive interactions in the new aeon (like if our absolute zero temperature was full of motion beneath the Planck scale, like part of a uniform vacuum - I'm improvising again...)

3. I don't know anything about quantum mechanics in general relativity, but once we let go of particle numbers and identities in quantum fields, it is not hard to imagine that light cones are not a hard restriction. I'm thinking of the measurement process that works instantaneosly on entangled particles far away, or off-shell "virtual particles" in Feynman's perturbation theory that are not bound to light cones. In these examples, it becomes clear that this might be just a technical issue of the maths employed, and I'm not sure at which level conformal cyclic cosmology is even compatible to quantum field theory at this stage... so still hoping for some answers by real experts.

Please downvote while leaving some comment from which I can learn, too :-)

Since no-one qualified would answer, I'll a give it a shot:

1. Talking quantum mechanics, these bosons have no identity, and their overall state does not even need to have a well-defined particle number in Fock space. This means, mathematically, the cosmic state of e.g. the photon field would be a superposition of one-, two-, three- ... gazillion-photon states, and each of them is symmetrised for particle location. So there is no particle Alice and particle Bob, just amplitudes/probabilities for some interacting in a given space-time volume. Apparently, this state would look like any other with arbitrary density because there is no measure for time and space, once everything is massless bosons.

2. Again, the particle number will be very fuzzy, and maybe very similar to some kind of vacuum with mostly "virtual particles" and such fluctuations (I'm improvising here). I had another question here about entropy. R. Penrose seems to try to get rid of it in evaporating black holes, but I (who am I?) was thinking that it doesn't matter if you have much entropy in microscopic degrees of freedom from the previous aeon that are so uniformely distributed that they don't drive interactions in the new aeon (like if our absolute zero temperature was full of motion beneath the Planck scale, like part of a uniform vacuum - I'm improvising again...)

3. I don't know anything about quantum mechanics in general relativity, but once we let go of particle numbers and identities in quantum fields, it is not hard to imagine that light cones are not a hard restriction. I'm thinking of the measurement process that works instantaneosly on entangled particles far away, or off-shell "virtual particles" in Feynman's perturbation theory that are not bound to light cones. In these examples, it becomes clear that this might be just a technical issue of the maths employed, and I'm not sure at which level conformal cyclic cosmology is even compatible to quantum field theory at this stage... so still hoping for some answers by real experts.

Please downvote while leaving some comment from which I can learn, too :-)