Cosmological gravitational particle production: Starobinsky vs Bogolyubov, uncertainties, and issues

We study production of free and feebly interacting scalars during inflation using the Bogolyubov coefficient and Starobinsky stochastic approaches. While the two methods agree in the limit of infinitely long inflation, the Starobinsky approach is more suitable for studying realistic situations, where the duration of inflation is finite and the scalar field has non-trivial initial conditions. We find that the abundance of produced particles is sensitive to pre-inflationary initial conditions, resulting in the uncertainty of many orders of magnitude. Nevertheless, a lower bound on the particle abundance can be obtained. High scale inflation is very efficient in particle production, which leads to strong constraints on the existence of stable scalars with masses below the inflationary Hubble rate. For example, free stable scalars are allowed only if they have masses below an eV or the reheating temperature is in the GeV range or below. We find universal scaling behavior of the particle abundance, which covers free and feebly interacting scalars as well as those with a small non-minimal coupling to gravity. These considerations are important in the context of non-thermal dark matter since inflationary particle production provides an irreducible background for other production mechanisms.