[Edit: I've just realized this is bordering on an essay, sorry.]
Going back to a difficulty with infinite recurrence theory, just based on a multiverse.
Leaving aside difficulties with the idea of infinity, let's say there are infinitely many temporally and spatially distinct universes (infinite because the hyperspace within which they exist is infinite, not because there are necessarily infinitely many different types of universes: ontological possibility is limited by quantum mechanical laws, and quantum mechanical laws operate within a limited though very large space of possibilities) which can never communicate with one another because they are receding from each other faster than light.
Let's also say that an indefinite number of those are 'identical' in the sense that their initial conditions, physical laws, and fine tuning of constants are the same, so exactly the same history will occur within exactly the same physical layout, same history on earth, same events, beings, consciousnesses etc.
It would seem that such a multiverse would actually preclude a type of eternal recurrence scenario, in which the same conscious beings have to live out the same lives over and over ad infinitum.
Why? Because there would be no universal meta-measure by which we could say that the events in universe a occur [earlier or later than] or [at the 'same time' as] events in 'identical' universes b, c, d, etc.
So say a conscious organism lives and dies in universe a. On multiverse theory, there will be an indefinite number of other universes b, c, d, etc in which that 'same' organism lives and dies, but unless we are willing to arbitrarily posit (somewhat ad hoc) some absolute metric time system which governs the whole multiverse (for which there is no actual evidence and which would violate relativity theory), there is no meaningful way in which we can apply the temporal properties of [later than], [earlier than] or [at the same time as] to describe possible inter-universe time relations between such conscious organisms.
By definition there can be no such relations, not even relative ones, because not even the speed of light can connect any two universes to allow common reference frames to be used.
Therefore there cannot be an infinitely or indefinitely recurring (one after the other in some kind of temporal sequence) series of 'identical' lives for any particular organism which occur in distinct yet 'identical' universes.
It seems to follow that everything that occurs from a first-person conscious perspective within the lifetime of an organism in a universe can only be experienced once, even if indefinite identical organisms in indefinite identical universes within the multiverse also exist. Assuming that the identity between organisms x, y. z, implies identity of conscious states, it cannot be the case that the same conscious states will be repeated for that organism in identical universes after that organism has died (since repetition, even subjectively experienced, implies temporal sequence, which cannot have any meaning in a multiverse).
It would seem that all the 'same' conscious states of the 'same' organism in the different 'identical' universes would collapse into one undifferentiated conscious state.
This isn't to say that there is some kind of absolute temporal simultaneity occurring between events and conscious states in identical yet spatio-temporally distinct universes, but only that [consciousness of x in universe a] = [consciousness of y in universe b] = [consciousness of c in universe z] etc.
It's a relation of ontological and phenomenological identity in which considerations of time/sequences/metric ordering etc. are meaningless and would constitute category errors as far as any known physical ideas of time are concerned.
Now, if you don't want to say that each 'identical' being/conscious experience x, y, z, (corresponding isomorphically to 'identical' universes a, b, c, etc.) is strictly ontological identical, but that the spatio-temporal separation of each 'identical' universe implies that each being is different if solely by virtue of its being in a spatio-temporally distinct universe, then this also seems to undermine infinite recurrence of the same experiences.
Because the departure from strict logical identity gives us no reason to suppose the 'same' conscious experience to repeat 'itself', since it occurs in a different spacetime within the multiverse manifold. We might say that that each token occurrence of the 'same' conscious experience instantiates a unique and single type (something like a platonic form), but that each token is distinct from every other token, just like every identical clone is distinct from every other identical clone, although all the clones conform to the same original genetic model.
In summary, there can be no before or after relation, or things happening at the 'same time' between universes on a multiverse model.
Time loses all meaning within the context of thinking about the possible relations of distinct universes within a multiverse.
So no infinite iterations from a first-person conscious perspective can be posited from this way of looking at the possibility of ER.
The notion of an iteration or sequence presuppose some form of time-ordering which I propose and argue cannot hold or have any meaning for a multiverse theory.
