Primordial black hole mass functions as a probe of cosmic origin

We discuss a novel window to probe the origin of our universe via the mass functions of primordial black holes (PBHs). The mass functions of PBHs are simply estimated using the conventional Press-Schechter formalism for two paradigms of cosmic origin, including inflationary $\Lambda$CDM and bounce cosmology. The standard inflationary $\Lambda$CDM model cannot generate an appreciable number of massive PBHs; however, non-trivial inflation models with blue-tilted power spectra at small scales and matter bounce cosmology provide formation mechanisms for heavy PBHs, which in turn, may seed the observed supermassive black holes (SMBHs). By fitting the SMBH mass functions at high redshift ($z \sim 6$) derived from Sloan Digital Sky Survey (SDSS) and Canada-France High-z Quasar Survey (CFHQS) quasars, for two paradigms of cosmic origin, we derive constraints on the PBH density fraction $f_{\mathrm{PBH}}$ at $z \sim 6$ and the characteristic mass $M_{\star}$, with the prior assumption that all SMBHs stem from PBHs. We demonstrate that this newly proposed procedure, relying on astronomical measurements that utilize deep-field surveys of SMBHs at high redshift, can be used to constrain models of cosmic origin. Additionally, although not the main focus of this paper, we evolve the mass function from $z\sim6$ to $z\sim0$ through an assumption of $3\times 10^8$-year Eddington's accretion, and give a rough estimation of $f_{\mathrm{PBH}}$ at $z \sim 0$.