The infinite space of the Universe

I don't think time is a comparison of cyclical events. Time is merely a comparison of events in general. Much like you can say "before I was born" and "after I was born." Any event has the ability to create at least a modicum of temporality, merely by being able to say "before" and "after."What a cycle does is exactly what the scythe clock in Death's house in Terry Pratchett's "Discworld" series does. It chops time up into smaller bits, giving us, essentially, many befores and afters, and because we now have more than one, betweens.

You've actually already stated why the cyclical theory has been "put on the back burner" for the time being: If the universe were going to reach a point and start collapsing again, the expansion would have to be slowing down, ultimately to come to a zero point before it starts accelerating back the other way.

Yes, it is. That's why the theory is sort of put on the back burner, as it were. It's not gone, and there are still proponents of it, but it requires more complexity to explain, and Occam's Razor would indicate that it's not the case.For one thing, Dark Energy would have to have the property of pushing things apart, faster and faster, until something makes it change and begins pulling things together again. This would seem to indicate two flavors of Dark Energy, one that pushes things apart and one that pushes things together. OR that gravity, which seems to be losing against Dark Energy now, will wipe the sweat from it's brow, get back in the fight and deliver an unexpected knock-out blow.