  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 $z
\sim 0$.

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology