Multi-messenger Probes of Inflationary Fluctuations and Primordial Black
  Holes
  Next generation cosmic microwave background spectral distortion and pulsar
timing array experiments have the potential to probe primordial fluctuations at
small scales with remarkable sensitivity. We demonstrate the potential of these
probes to either detect signatures of primordial black holes (PBHs) sourced
from primordial overdensities within the standard thermal history of the
universe over a 13-decade mass range ${\cal O}(0.1-10^{12})M_\odot$, or
constrain their existence to a negligible abundance. Our conclusions are based
only on global cosmological signals, and are robust under changes in i) the
statistical properties of the primordial density fluctuations (whether Gaussian
or non-Gaussian), ii) the merger and accretion history of the PBHs and
assumptions about associated astrophysical processes, and iii) clustering
statistics. Any positive detection of enhanced primordial fluctuations at small
scales would have far-reaching implications from the content of dark matter to
origin of BHs in the centers of galaxies, and to the field content of the
inflation. On the other hand, their non-detection would also have important
corollaries. For example, non-detection up to forecast sensitivities would tell
us that PBHs larger than a fraction of a solar mass can constitute no more than
a negligible fraction of dark matter. Moreover, non-detection will also rule
out the scenario that PBHs generated by primordial overdensities could be the
progenitors of super-massive black holes (SMBHs), of topical interest as there
are only a few widely accepted proposals for the formation of SMBHs, an even
more pressing question after the detection of active galactic nuclei over a
billion solar masses at redshifts $z \geq 7$. Finally, non-detection sets the
strongest bounds on the amplitude of small scale inflationary fluctuations for
over 6 decades.
