Keep believing that budy. Joking.

It is someone with the same exact experience and memories as you. That is if the big bounce theory is true.

We run into a similar problem with cloning, if you clone yourself is that clone is you, an extension of you or someone else altogether. At least in the case of cloning, we know that over time that clone would be different from you as time passes.

In the case of a big bounce theory, if we assume that the universe is deterministic, we get the same exact outcome every time.