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Next generation cosmic microwave background spectral distortion and pulsartiming array experiments have the potential to probe primordial fluctuations atsmall scales with remarkable sensitivity. We demonstrate the potential of theseprobes to either detect signatures of primordial black holes (PBHs) sourcedfrom primordial overdensities within the standard thermal history of theuniverse over a 13-decade mass range ${\cal O}(0.1-10^{12})M_\odot$, orconstrain their existence to a negligible abundance. Our conclusions are basedonly on global cosmological signals, and are robust under changes in i) thestatistical properties of the primordial density fluctuations (whether Gaussianor non-Gaussian), ii) the merger and accretion history of the PBHs andassumptions about associated astrophysical processes, and iii) clusteringstatistics. Any positive detection of enhanced primordial fluctuations at smallscales would have far-reaching implications from the content of dark matter toorigin of BHs in the centers of galaxies, and to the field content of theinflation. On the other hand, their non-detection would also have importantcorollaries. For example, non-detection up to forecast sensitivities would tellus that PBHs larger than a fraction of a solar mass can constitute no more thana negligible fraction of dark matter. Moreover, non-detection will also ruleout the scenario that PBHs generated by primordial overdensities could be theprogenitors of super-massive black holes (SMBHs), of topical interest as thereare only a few widely accepted proposals for the formation of SMBHs, an evenmore pressing question after the detection of active galactic nuclei over abillion solar masses at redshifts $z \geq 7$. Finally, non-detection sets thestrongest bounds on the amplitude of small scale inflationary fluctuations forover 6 decades.

Multi-messenger Probes of Inflationary Fluctuations and Primordial Black Holes