Yes it does. Consider the following [preferrably after green refreshments]:
Our universe was birthed as an explosion, and particles expand outward. Yet even if they approach an infinite amount of space between each there will remain an gravitational attraction between all particles that will bring them back together given enough time, and will return to the original configuration before the explosion.
At that point the explosion will recur.
You could plot the progress of those universes superimposed on one another and call it parallel. Which goes well with a mathematical model since the expansion and contraction is inherently and pervasively sinusoidal.
However that isn't a great approach as far as trying to navigate between them. You can't exactly "go back" like you would expect two independent functions, so the idea of what we could accomplish is more nuanced.
You could however consider that such a configuration doesn't result in "infinite" possibilities per se. The particles emerging from the big bang have certain properties, they combine in a certain way, and the major elements of the process are measurable and repeatable to some extent.
So instead if we were to plot it out each successive universe there would be a certain "wobble". Each iteration of the universe would be slightly different. If you know enough about the characteristic frequency of the wobble you could even move "back" and forth, although instead of going "back" you'd simply enter another iteration of the universe that is identical to a historical target.
Really this is the only way time travel is possible. You would have to position yourself to arrive at November 5, 1955 in a future universe identical to the current iteration.
Not exactly what you think of as time travel, but the only possible way it could work. And no, time paradoxes are silly and don't exist in this. If you "go back in time" and kill your grandfather you're only adding an additional harmonic to the characteristic frequency of the wobble of the universal life cycle. Instead of a progression of:
[exist in this universe], [exist in this universe]
[exist], [don't exist because you came here and killed your grandpa], [exist], [don't exist because you ...],...
And each interaction (or communication) adds an order of magnitude of complication of this harmonic. So the more interuniversal communication happens the harder it gets each time to calculate that "identical universe". In fact we could probably mathematically prove that it impossible to obtain such an identical universe after a certain amount of communication occurs for some meaningless constant which has likely already been surpassed by an infinite amount.
The reason that the communication is important is because if it didn't occur then we would be basically be trapped in a Star Trek-like where time simply loops, and we repeat the same actions over and over again for infinity. The communication/cross-contamination/what have you gives us the ability to pass on progress forward and have a evolving paradigm.