Two Pathways of Primordial Cloud Collapse: Fragmentation versus Direct Collapse under Enhanced Vacuum Energy

We explore the consequences of a specific hypothetical scenario for primordial cloud collapse at redshift z ~ 12. The scenario rests on three conditional premises: (1) that the cosmological constant Λ and the quantum vacuum energy density ρ_vac are physically distinct quantities; (2) that if distinct, ρ_vac was denser in the early universe by a factor (1+z)³ ≈ 2,000; and (3) that if such a denser vacuum existed, there is a mechanism by which it exerts net inward pressure on matter concentrations. None of these premises is established. We do not claim to prove them. We ask: if all three hold, what happens to a primordial gas cloud?

A single cloud (M ~ 10⁵ M☉, T ~ 10⁴ K) is traced under three conditions:

• Scenario A (trace metallicity, standard vacuum): Dust-induced cooling triggers fragmentation into a stellar cluster with remnant black holes of ~10–100 M☉.
• Scenario B (zero metallicity, standard vacuum): The well-established direct-collapse pathway produces a supermassive star and a ~10⁴–10⁵ M☉ seed, but requires a fine-tuned Lyman–Werner radiation source.
• Scenario C (zero metallicity, enhanced vacuum pressure): The hypothetical vacuum confinement provides an additional, isotropic compression mechanism that may reduce the Lyman–Werner requirement and accelerate the collapse timescale.

Scenarios A and B are established control cases from the existing literature. Scenario C is the new, conditional contribution. Its unique prediction is not faster growth but higher abundance of direct-collapse seeds—if the premises hold, vacuum pressure acts on every cloud at a given epoch, circumventing the fine-tuned requirement for a nearby UV source that limits seed abundance in standard models.

All calculations use established physics—Jeans instability, Bonnor–Ebert stability, Salpeter accretion—with the sole addition being the enhanced vacuum energy density at high redshift. Results are parametrized by the dimensionless ratio η = ΔP_vac / P_cloud, making the dependence on the unknown ρ_vac,0 transparent. The paper identifies the regimes where the analytical framework applies (η ~ 0.1–1) and where it breaks down (η ≫ 1), and confronts the companion framework's own predicted ρ_vac,0 honestly against these regimes.

The model is falsifiable: if the sequestering hypothesis is excluded by CMB data, if simulations show external pressure does not relax the Lyman–Werner requirement, or if ρ_vac,0 is independently measured and found to be too small, the conditional prediction fails.

Keywords: vacuum energy, direct collapse black hole, primordial gas cloud, Jeans instability, Bonnor–Ebert mass, supermassive star, early universe, JWST, structure formation, fragmentation, conditional model

Companion papers:

• Kriger, B. (2026). On Quantum Vacuum Energy, Cosmological Constant and Missing Mass. https://doi.org/10.5281/zenodo.18943014
• Kriger, B. (2026). Known Properties of Vacuum Energy, Dark Matter and JWST Early Galaxy Formation. https://doi.org/10.5281/zenodo.18942968
• Kriger, B. (2026). What If the Vacuum Gravitates? A Reinterpretation of ΛCDM That Might Resolve Its Paradoxes. https://doi.org/10.5281/zenodo.18946637
• Kriger, B. (2026). Matter-Dependent Vacuum Energy Density and Inhomogeneous Cosmic Expansion. https://doi.org/10.5281/zenodo.18896536
• Kriger, B. (2026). The Frozen Universe Illusion: Temporal Resolution as a Fundamental Limit on Cosmological Observation and SETI. https://doi.org/10.5281/zenodo.18901492