Act 1 Collapse
The perfectly still lake begins to drain. Gravity pulls the superfluid inward — and because the fluid is frictionless, every bit of energy converts perfectly into motion. Nothing is wasted.
Gravitational Collapse
Hundreds of particles fall inward under gravity, accelerating as density grows at the center.
The Frictionless Bowl
Somewhere — it does not matter where — a region of the fluid is slightly denser than its neighbors. Gravity notices. The fluid creeps toward that point, imperceptibly at first, then faster. And faster. A whirlpool forms.
But this is no ordinary whirlpool. In a bathtub, the water loses energy to friction against the walls, against itself, against the drain. Here, there are no walls. And the fluid is a superfluid — below a critical velocity, it cannot lose energy at all.
Think of a ball bearing rolling down a frictionless bowl. It picks up speed with perfect efficiency. That is what happens here, except the "bowl" is the gravitational potential well carved by the fluid's own mass, and the "ball bearing" is the fluid itself. It deepens the well as it falls, which makes it fall faster, which deepens the well further.
Runaway collapse.
The remnant left behind — the regions too diffuse to participate — becomes the pre-existing superfluid floor that fills the space between galaxies today.
Frictionless Gravitational Infall
The collapse has two key features that distinguish it from ordinary gravitational collapse:
1. The Landau Criterion
In a superfluid, excitations (heat, friction, sound) cannot be created below a critical velocity $v_c$. This is the Landau criterion — the most fundamental property of superfluidity. Below $v_c$, the fluid flows without dissipation.
For the universal fluid, $v_c$ is set by the gap in the excitation spectrum. As long as the infall velocity $v < v_c$, the collapse is lossless: every bit of gravitational potential energy converts to kinetic energy with 100% efficiency.
2. Violent Relaxation
The collapse proceeds via violent relaxation (Lynden-Bell 1967): the time-varying gravitational potential redistributes energy among fluid elements without two-body collisions. This is the standard mechanism for collisionless gravitational collapse — and it works even better in a superfluid where there truly is zero friction.
The key point: violent relaxation doesn't need collisions. It needs a rapidly changing gravitational potential. The self-gravitating collapse provides exactly that.
What's left behind
Not everything collapses. The outermost, most diffuse regions don't participate — their density is too low for gravity to overcome the fluid's support. These remnant regions become what we'll later call Zone 3: the pre-existing superfluid floor filling intergalactic space.
Derivation: Why the Infall Is Lossless
An object moving through a superfluid at velocity $v$ can only create an excitation of momentum $p$ and energy $\varepsilon(p)$ if:
$$v > v_c = \min_p \frac{\varepsilon(p)}{p}$$The excitation spectrum is:
$$\varepsilon(p) = \sqrt{c_s^2 p^2 + \left(\frac{p^2}{2m}\right)^2}$$The minimum of $\varepsilon(p)/p$ occurs at $p \to 0$, giving $v_c = c_s = c/\sqrt{3}$.
The infall velocities during the initial collapse phase are non-relativistic ($v \ll c$), so $v \ll v_c = c/\sqrt{3}$. The Landau criterion is satisfied everywhere. No excitations are created. No energy is dissipated.
Violent Relaxation Timescale
The relaxation time for violent relaxation is:
$$t_{\text{relax}} \sim t_{\text{cross}} \sim \frac{1}{\sqrt{G\bar{\rho}}}$$The rapidly changing gravitational potential $\Phi(t)$ does work on particles: $\Delta E = \int \dot{\Phi}\, dt$. This redistributes energy among fluid elements without requiring collisions. In a superfluid, where there truly are no collisions, this is the only relaxation mechanism — and it's sufficient.
Expert Notes
Comparison with CDM collapse
In $\Lambda$CDM, dark matter collapse proceeds similarly — it's also collisionless — but for a different reason. CDM particles are collisionless because their cross-section is tiny. The universal fluid is collisionless because it's a superfluid: the Landau criterion forbids dissipation below $v_c$. The mathematical description is identical; the physical mechanism is different.
Angular momentum and the detonation asymmetry
The pre-collapse fluid has angular momentum (from tidal torques in the ambient medium). This angular momentum is conserved during the frictionless collapse, concentrating into the central region. The asymmetry it produces — different energy densities in different directions — will become the non-uniformity of the detonation in Act 3, which ultimately becomes the CMB anisotropy pattern.
The Zone 3 remnant
The uncollapsed remnant (Zone 3) has density $\rho_3 \sim 10^{-30}$ g/cm$^3$ — the same order as the observed intergalactic medium density. This is the superfluid floor. It remains in the ground state, continues to be frictionless and achromatic, and provides the medium through which light propagates. Its equation of state ($\gamma = 2$) determines the long-range gravitational behavior that standard cosmology attributes to "dark matter."
Interactive: Gravitational Potential Well
Watch the potential well deepen as the superfluid collapses. Gold: the fluid density profile. Blue dashed: what happens with friction (energy is lost, collapse is less efficient). The frictionless superfluid converts 100% of potential energy to kinetic energy.
What Comes Next
The collapse concentrates energy to enormous density. When the concentration crosses a critical threshold — the Schwarzschild limit — a primordial seed forms. Three independent calculations will converge on its size.