I've skimmed the paper and it's quite readable. The problem arises because probability doesn't make sense in an infinite universe. To make sense of it the autho

I've skimmed the paper and it's quite readable. The problem arises because probability doesn't make sense in an infinite universe. To make sense of it the authors consider a small patch of finite size and then let that finite size go arbitrarily large. In this picture probability is well defined but our space and time will always have an edge. However this is just a model, not an expected version of reality. The same thing happens in quantum field theory where the theory doesn't make sense at arbitrarily high energy so we just impose a cut off and ignore energies above a certain scale. This doesn't mean we think physics just stops there. Instead, it's just a way to parameterise our ignorance about what comes beyond.