Act 2 The Primordial Black Hole

The Whirlpool Reaches Critical

The whirlpool tightens. The density at the center climbs toward infinity. And then something familiar happens: the concentration of mass crosses the Schwarzschild threshold, and a black hole forms.

Not a stellar remnant. Not a supermassive monster at a galactic center. A primordial black hole, born from the collapse of the superfluid itself.

How big? About 24 megaparsecs across. That sounds enormous, and it is. But here is the twist: we are still inside it. The observable universe is the interior of this structure, distended by the explosion that comes next. Every galaxy you have ever seen, every photon in the CMB, every atom in your body — all of it was once compressed inside this 24 Mpc sphere.

Three calculations, one answer

The size isn't guessed. Three completely independent calculations converge on the same number:

1. The BAO fundamental note — the baryon acoustic oscillation scale interpreted as the lowest acoustic mode of a cavity
2. The observable universe mass — plug in $M \sim 10^{53}$ kg and compute the Schwarzschild radius
3. Planck-time self-consistency — at the Planck time, the black hole fills its own horizon

All three give $R_s \sim 24$ Mpc comoving. When three independent methods agree, you should pay attention.

The Three Convergent Size Calculations

Calculation 1: BAO as a fundamental acoustic mode

The baryon acoustic oscillation (BAO) scale — about 150 Mpc comoving — is the most precisely measured distance in cosmology. In standard cosmology, it's the sound horizon at baryon drag epoch.

In UFC, the BAO scale is the fundamental acoustic mode of the primordial seed cavity. A standing wave in a spherical cavity of radius $R$ has its fundamental mode at wavelength $\lambda \sim 2\pi R$. The BAO scale of ~150 Mpc corresponds to $R_s \sim 150/(2\pi) \sim 24$ Mpc.

Calculation 2: Schwarzschild radius from total mass

The total mass-energy of the observable universe is approximately $M_{\text{obs}} \sim 10^{53}$ kg. The Schwarzschild radius is:

This is a straightforward GR calculation — the same formula used for any black hole.

Calculation 3: Planck-time self-consistency

At the Planck time ($t_P \sim 5.4 \times 10^{-44}$ s), the Hubble horizon is $c \cdot t_P \sim 1.6 \times 10^{-35}$ m. A primordial seed with $R_s \sim 24$ Mpc comoving, when traced back to the Planck epoch, has a physical size that matches the Planck-time horizon: $R_s / R_{\text{horizon}} \sim 1$.

The black hole fills its own causal horizon at the Planck time — it is as large as it possibly can be.

The convergence

Three completely different approaches — acoustic, gravitational, quantum — all give $R_s \sim 24$ Mpc. This is the size of the structure that detonates to produce the Big Bang.

Derivation: The Schwarzschild Radius

Derivation: BAO as Fundamental Mode

Expert Notes

We are inside the black hole

This is the most counterintuitive claim in UFC: the observable universe is the interior of a black hole. But this is less exotic than it sounds. The interior of a Schwarzschild black hole is a valid FRW spacetime (Oppenheimer-Snyder 1939). The detonation that follows (Act 3) converts the collapse into expansion — the time-reverse of gravitational collapse, driven by the CJ detonation energy.

Not a white hole

UFC does not invoke white holes (the time-reverse of a black hole). The expansion is driven by a physical process — detonation — not by a reversal of time's arrow. The distinction matters: a white hole is a vacuum solution with no mechanism; a detonation is a driven process with well-understood physics.

Comparison with cosmological Jeans length

The Jeans length at the pre-detonation density $\rho_0$ is:

For $c_s = c/\sqrt{3}$ and $\rho_0$ corresponding to $M_{\text{obs}}$ within $R_s$: $\lambda_J \sim R_s$. The primordial seed is one Jeans mass. This is the maximum stable mass — anything larger fragments, anything smaller doesn't collapse. The single primordial structure is not a coincidence; it's the Jeans criterion at cosmological density.

The quality factor

This is a one-shot detonation, not a cyclic process. The quality factor $Q \approx 0.94$ (from the conversion efficiency of the reaction zone) means 94% of the fuel energy goes into the blast. There is no "previous cycle" and no "bounce" — the detonation is irreversible.