Natural Supercooling and Reheating along Supersymmetric Flat Directions and Observable Gravitational Waves at the Einstein Telescope and the Cosmic Explorer

We study supercooled first-order phase transitions in a supersymmetric hidden sector with a spontaneously broken $U_X$, focusing on the frequency range of the Einstein Telescope and Cosmic Explorer. The new analysis still awaits peer review, but it already lays out the central claim clearly.

This 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. We study supercooled first-order phase transitions in a supersymmetric hidden sector with a spontaneously broken $U(1)_X$, focusing on the frequency range of the Einstein. Along the D-flat direction the tree-level quartic vanishes, so the barrier is generated radiatively by soft SUSY-breaking splittings.

In the $\overline{\rm DR}$ scheme the gaugino mass $M_{\tildeλ}$ sets the barrier depth, while the soft scalar mass $m_0$ stabilizes the broken vacuum. For $M_{\tildeλ}/v_X\simeq0.05$--$0.23$, the predicted signal reaches $Ω_{\rm GW}h^2\sim3\times10^{-10}$ near the percolation boundary.

We follow this evolution with an 11-variable Boltzmann system that separates the cold nucleating exterior from the reheated true-vacuum interior. Reheating mainly enters through the energy budget and redshift factors.

The same hidden sector can reproduce $Ω_{\rm CDM}h^2=0.12$ through relativistic dark-quark freeze-out followed by entropy dilution from hidden-Higgs decay, with. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy.

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.

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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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