We study production of primordial black holes ( PBHs ) during an early matter-dominated phase .
As a source of perturbations , we consider either an inflaton field with a running spectral index or a spectator field that has a blue spectrum and thus provides a significant contribution to PBH production at small scales .
First , we identify the region of the parameter space where a significant fraction of the observed dark matter can be produced , taking into account all current PBH constraints .
Then , we present constraints on the amplitude and spectral index of the spectator field as a function of the reheating temperature .
We also derive constraints on the running of the inflaton spectral index , { d } n / { d } { ln } k \lesssim 0.001 , which are comparable to those from the Planck satellite for a scenario where the spectator field is absent .