DRUMS Theory · Early Galaxy Formation in DRUMS

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1. Cosmological Superfluid Field

The DRUMS ontology models the universe as a coherent superfluid described by:

\[ \Psi(\mathbf{x},t) = \sqrt{\rho(\mathbf{x},t)} \, e^{i\theta(\mathbf{x},t)} \]

The velocity field arises from the phase gradient:

\[ \mathbf{v} = \frac{\hbar}{m} \nabla\theta \]

2. Governing Dynamics

Evolution follows superfluid hydrodynamics, beginning with the continuity equation:

\[ \frac{\partial\rho}{\partial t} + \nabla \cdot (\rho\mathbf{v}) = 0 \]

and the modified Euler equation including quantum pressure:

\[ m\left( \frac{\partial\mathbf{v}}{\partial t} + (\mathbf{v} \cdot \nabla)\mathbf{v} \right) = -\nabla(P + Q + V_{\text{eff}}) \]

where the quantum pressure term is defined as:

\[ Q = -\frac{\hbar^2}{2m} \frac{\nabla^2\sqrt{\rho}}{\sqrt{\rho}} \]

The effective potential \(V_{\text{eff}}\) incorporates the emergent gravitational interaction arising from the superfluid's vortex dynamics and the cubic magnetic substrate.

3. Linear Growth of Perturbations

To study structure formation, we introduce small perturbations around the mean background density:

\[ \rho = \rho_0 + \delta\rho \]

Linearizing the governing equations yields a wave equation for the density perturbation:

\[ \frac{\partial^2 \delta\rho}{\partial t^2} = c_s^2 \nabla^2 \delta\rho - G_{\text{eff}} \rho_0 \delta\rho \]

Here \(c_s\) is the sound speed in the superfluid, and \(G_{\text{eff}}\) is the effective gravitational coupling strength that emerges from the substrate and vortex interactions.

4. Jeans Instability and the Fragmentation Scale

Instability occurs for wavelengths larger than the Jeans scale:

\[ k^2 < k_J^2 = \frac{G_{\text{eff}}\rho_0}{c_s^2} \]

The characteristic fragmentation scale for the first collapsed structures is therefore:

\[ \lambda_J = \frac{2\pi}{k_J} \]

This scale sets the typical mass and size of the earliest galaxies — not as an input parameter, but as an emergent output of the superfluid's intrinsic properties.

                        The first galaxies are not formed by dark matter collapse. They are the first coherent vortical structures to emerge from the superfluid Jeans instability.
                    

5. Role of the Substrate in Structure Growth

The cubic magnetic substrate influences early galaxy formation in two important ways:

Anisotropic collapse: The substrate's lattice directions introduce a preferred orientation for perturbation growth, seeding the large-scale alignment of galaxies and filaments.
Quantized mass scales: The substrate's resonance hierarchy — spanning 44 orders of magnitude — imprints discrete mass scales on the collapsing superfluid, explaining the observed galaxy mass function.

Without dark matter, the DRUMS framework predicts that the first galaxies should form earlier and with a characteristic mass scale set by the superfluid's coherence length at recombination. This prediction is currently being tested by JWST observations of high-redshift galaxies.

6. Comparison with Standard ΛCDM

The DRUMS interpretation of early galaxy formation differs fundamentally from the standard ΛCDM picture:

No dark matter: Structure is seeded directly by superfluid instabilities, not by dark matter overdensities.
Emergent gravity: The gravitational instability term \(G_{\text{eff}}\) is not a fundamental constant but a local property of the superfluid and substrate.
Quantized scales: The galaxy mass function is shaped by the substrate's resonance hierarchy, not by hierarchical dark matter merging.
Earlier formation: The absence of dark matter suppression allows galaxies to form at higher redshifts, potentially explaining the unexpectedly mature galaxies observed by JWST.

“In DRUMS, the first galaxies are not assembled from dark matter halos — they crystallise directly from the superfluid.”

Conclusion: Galaxies as Superfluid Condensates

In the DRUMS framework, early galaxy formation emerges directly from the superfluid dynamics of the universe. The Jeans instability of the superfluid condensate produces the first collapsed structures, with their characteristic mass scale set by the superfluid's intrinsic coherence length — not by an external dark matter scaffolding.

This interpretation provides a natural explanation for the observed early emergence of massive galaxies in the James Webb Space Telescope's deep fields. Those galaxies are not an anomaly requiring late-time dark matter assembly; they are the first coherent vortical structures of the superfluid — the galaxy-scale analogues of the quantised vortices that appear in laboratory superfluids.

Every galaxy is a frozen superfluid vortex. The first galaxies were the first such vortices to emerge from the Jeans instability, and the entire cosmic web — from the smallest dwarf galaxy to the largest cluster — is the fossilised record of the superfluid's collapse. In this reading, the question "how did the first galaxies form?" is not a separate problem requiring exotic initial conditions. It is answered by the same superfluid dynamics that explain everything else: the CMB anomalies, the baryon asymmetry, and the origin of gravity itself.