Numbers aside, there is nothing in our universe that suggests that we shouldn't take the concept of future timelike infinity seriously, and some evidence that w

Numbers aside, there is nothing in our universe that suggests that we shouldn't take the concept of future timelike infinity seriously, and some evidence that we should, notably the accelerating metric expansion of space. That in turn gives us a receding horizon, which gives us Unruh radiation, which gives us fluctuations (and there are other sources for those), and that in turn poses all sorts of theoretical problems ranging from outright Poincaré recurrence to "mere" Boltzmann brains. Getting rid of these when you take infinity seriously is a theoretical challenge. If we could prove that the universe will not expand forever, that would be a nice outcome of research in physical cosmology.