Reconstructing Early Primordial Black Hole Domination from Gravitational-Wave Backgrounds

Primordial Black Holes with masses below $\mathcal{O}$g occupy an interesting region of parameter space that is largely inaccessible to conventional observations. The new analysis still awaits peer review, but it already lays out the central claim clearly.

It matters because astrophysics becomes persuasive only when an observed signal can be tied to a physically defensible explanation. Compact objects such as neutron stars and black holes are natural laboratories for extreme physics, but the distance and complexity of these systems make interpretation difficult without multi-wavelength coverage and careful modeling. A detection without a mechanism is only half a result. the other half comes from showing that the signal fits quantitatively inside a coherent physical picture rather than merely being consistent with a broad family of models. Primordial Black Holes (PBHs) with masses below $\mathcal{O}(10^9)$g occupy an interesting region of parameter space that is largely inaccessible to conventional observations. Despite evaporating before Big Bang Nucleosynthesis (BBN), these PBHs can naturally generate a period of early matter domination in the early Universe.

A primordial gravitational-wave background (GWB) provides a window onto this otherwise inaccessible regime, since the modified expansion history leaves a characteristic spectral. The locations of these characteristic frequencies can be used to reconstruct the underlying PBH parameters, in particular the PBH mass.

For a freely propagating GWB, the location of these frequencies additionally allow the initial PBH abundance to be determined. We derive simple numerical relations that map these characteristic frequencies directly onto the PBH mass and initial abundance.

Future GW experiments span a vast frequency range, providing sensitivity to PBH masses from the BBN bound of $\mathcal{O}(10^9)\, \mathrm{g}$ down to the lower bound of. We find that the nanohertz signal reported by NANOGrav, if primordial in origin, is already probing PBH masses in the range $4$--$90\, \mathrm{Mg}$.

The broader interest lies in turning an observational clue into something that can be weighed against competing models of the underlying physics. Astrophysics does not have the luxury of controlled experiments; everything is inferred from radiation that traveled across cosmic distances under conditions that cannot be reproduced in a terrestrial laboratory. This makes the interpretation chain longer and more uncertain than in bench science, but it also means that a well-constrained measurement of an extreme object carries theoretical information that no earthbound experiment can provide.

GW observations therefore offer access to a vast region of PBH parameter space that is otherwise beyond the reach of current experiments. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy.

Because this is still a preprint, the result should be read with genuine interest and proportionate caution. Peer review is not a guarantee of correctness, but it is a process that forces authors to respond to technical criticism from specialists who have no stake in a particular outcome. Preprints that survive that process, often with substantive revisions, emerge with a stronger evidential base than the version that first appeared. Until that stage is complete, the responsible reading keeps uncertainty explicitly visible rather than treating the claims as established findings.

The next step is to see whether independent datasets and physical modeling converge on the same interpretation. Multi-wavelength follow-up, combining X-ray, radio and optical data where possible, is typically what separates a compelling detection from a robust physical characterization. In high-energy astrophysics, results that initially looked definitive have been revised when data from a second messenger arrived; the current result should be read with that history in mind. Until peer review and independent follow-up address those open questions, skepticism is not a failure of appreciation for the work; it is part of how science decides what to keep.

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