  In this work we present a novel approach to the study of cosmological
particle production in asymptotically Minkowski spacetimes. We emphasize that
it is possible to determine the amount of particle production by focusing on
the mathematical properties of the mode function equations,i.e. their
singularities and monodromies, sidestepping the need to solve those equations.
We consider in detail creation of scalar and spin 1/2 particles in four
dimensional asymptotically Minkowski flat FLRW spacetimes. We explain that when
the mode function equation for scalar fields has only regular singular points,
the corresponding scale factors are asymptotically Minkowski. For Dirac spin
1/2 fields, the requirement of mode function equations with only regular points
is more restrictive, and picks up a subset of the aforementioned scale factors.
For the scalar case, we argue that there are two different regimes of particle
production; while most of the literature has focused on only one of these
regimes, the other regime presents enhanced particle production. On the other
hand, for Dirac fermions we find a single regime of particle production.
Finally, we very briefly comment on the possibility of studying particle
production in spacetimes that don't asymptote to Minkowski, by considering mode
function equations with irregular singular points.
