The relevant part is at the end. Essentially, given enough time, quantum effects will result in an entire new universe spontaneously popping into existence. That time is ~10^(10^(10^56)).[0]
But, the number of ways that all particles in the universe can be arranged is only ~10^(10^115). That number is much smaller than the time to just go 'pop, new universe'. So, the much larger number also becomes about the time it takes to just have a new universe identical to our current one just go 'pop, new universe'.
The other entries in that article are just as joyously mind-bending. I really really love that page!
https://en.wikipedia.org/wiki/Timeline_of_the_far_future
[0] Side note: The time for a 'Boltzmann Brain' (a consciousness that just floats in the infinite void thinking away, somehow) to spontaneously appear is only ~10^(10^50).
EDIT: Changed Fat to Far
Also, I forgot to mention that all these timelines are in years.
But then I thought about it and about any human unit of time really doesn't change the numbers much at all. Heck, even measured as units of 'age-of-the-current-universe', the extra 0s just fade into the rounding errors very quickly.
To be clear here, that is stating that however you measure time pretty much has no meaning at these scales.
As the Wikipedia page[0] puts it:
> Although listed in years for convenience, the numbers beyond this point are so vast that their digits would remain unchanged regardless of which conventional units they were listed in, be they nanoseconds or star lifespans.
0: https://en.wikipedia.org/wiki/Timeline_of_the_far_future#cit...
The theory is more that with "infinite" expansion, the universe becomes so spread out as to in spot become emptier than the vacuum energy, and a new universe spontaneously erupts in that low energy locale. In a very small nutshell.