Primordial Black Holes from Slow Phase Transitions with Delayed Reheating: A Peak-Theory Approach

The new analysis still awaits peer review, but it already lays out the central claim clearly.

It matters because cosmology operates at the edge of what current instruments can measure, where systematic errors and model assumptions are never trivial. Small discrepancies between independent measurements have historically pointed toward missing physics rather than simple calibration errors, and the ongoing tension in the Hubble constant is a live example of how a persistent disagreement between methods can reshape the theoretical landscape. Each new dataset that approaches this territory with independent systematics adds real information to a problem that has resisted easy resolution for more than a decade. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. ArXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community. Since delayed reheating results in an early matter-dominated phase between percolation and reheating, we developed a peak-theoretic approach to PBH formation during this phase.

To obtain the collapse probability, we performed large-scale Monte Carlo simulations and employed the hoop-conjecture criterion. We include tidal-torque terms to investigate the initial spin of the PBHs and find that the average spin parameter is $\mathcal{O}(10^{-3})$.

Furthermore, we obtain an emergent overdensity threshold for collapse that depends on the phase transition properties and reheating efficiency. We find that the resulting PBH abundance is extremely sensitive to the reheating efficiency, with order-unity changes in efficiency leading to variations of many orders of.

The relevance goes beyond one dataset because even small shifts in measured parameters can matter when the field is testing the limits of the standard cosmological model. The Lambda-CDM framework describes the observable universe with remarkable economy, but its success rests on two components, dark matter and dark energy, whose physical nature remains entirely unknown. Any credible measurement that tightens or loosens the constraints on those components moves the entire theoretical enterprise forward, regardless of whether the immediate result looks dramatic on its own terms.

We identify regions of parameter space where the resulting PBHs can account for the entirety of the dark matter abundance. Finally, we also constrain the phase transition and reheating properties from current data on (non-)observations of PBHs.

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 the effect survives when independent surveys, different calibration strategies and tighter control of systematic uncertainties enter the picture. Programmes such as Euclid, DESI and the Rubin Observatory will deliver datasets over the next several years that cover the same parameter space with largely independent methods. If the current signal persists through those tests, its theoretical implications will become impossible to set aside. 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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