  We study the spherically symmetric collapse of a real, minimally coupled,
massive scalar field in an asymptotically Einstein-de Sitter spacetime
background. By means of an eikonal approximation for the field and metric
functions, we obtain a simple analytical criterion---involving the physical
size and mass scales (the field's inverse Compton wavelength and the spacetime
gravitational mass) of the initial matter configuration---for generic
(non-time-symmetric) initial data to collapse to a black hole. This analytical
condition can then be used to place constraints on the initial primordial black
hole spectrum, by considering spherical density perturbations that re-entered
the horizon during an early matter-dominated phase that immediately followed
inflation.
