Milne-like spacetimes and their role in Cosmology

Abstract

Milne-like spacetimes are a class of FLRW models which admit $C^0$ spacetime extensions through the big bang. The boundary of a Milne-like spacetime can be identified with a null cone in the extension. We find that the comoving observers all emanate from a single point in the extension. This suggests that something physical may have happened there. Next we ask what role these spacetimes have in modern cosmology. We find that Milne-like spacetimes are inconsistent with classical cosmology theory in which a radiation-dominated era follows immediately after the big bang. However, Milne-like spacetimes are consistent with inflationary theory. In fact the very nature of Milne-like spacetimes solves the horizon problem. We note that this has already been observed for the Milne universe in [2] and [25]. Next we show, assuming a finite initial condition on the energy density, that Milne-like spacetimes naturally exhibit a slow-roll inflationary era. This makes Milne-like spacetimes good models for inflationary theory. We also show that Milne-like spacetimes still admit $C^0$ extensions under well-behaved perturbations.