Dark Matter from quasi-de Sitter Horizons

Assuming that (1) the universe underwent a post-inflationary accelerated expansion phase driven by a fluid with equation of state $P=w\rho$ and $-1<w<-1/3$, that (2) the cosmic horizon in an accelerating, quasi-de Sitter universe has a temperature inversely proportional to the proper size of the horizon, and that (3) we are static observers, we calculate the frozen-in density of a stable particle of mass $m$ produced by the cosmic horizon that does not undergo any number-changing processes in the late universe. We find that, as a function of the equation of state and the temperature when radiation domination starts and the quasi-de Sitter phase ends, the mass of the dark matter producing the observed cosmological abundance via this mechanism ranges from 10 keV up to close to the Planck scale.