Baryon Acoustic Oscillation Scale in DRUMS

Superfluid Field Description

The DRUMS framework models the cosmological medium as a coherent superfluid, described by a macroscopic wavefunction:

The superfluid velocity field is given by the gradient of the phase:

This fundamental description replaces the standard fluid approximation with a coherent quantum condensate, providing the medium for cosmological perturbations.

Linear Perturbations

Consider density perturbations around the mean background density:

Linearizing the continuity and Euler equations for the superfluid yields a wave equation for the density perturbation:

This is the fundamental equation describing the propagation of acoustic waves in the superfluid medium.

Effective Sound Speed

The effective sound speed in the superfluid arises from both pressure terms and quantum corrections:

At large scales — the regime relevant for BAO — the dominant term defines a characteristic propagation velocity that is nearly constant across cosmic history.

Acoustic Horizon Formation

The characteristic BAO scale emerges from the maximum distance that acoustic waves can travel between the Big Bang and the epoch of recombination:

where \(t_*\) is the time of decoupling. This horizon scale is imprinted in the distribution of matter as a preferred clustering length.

“The BAO scale is not a fixed length — it is the frozen imprint of how far phase coherence could travel before the universe became neutral.”

DRUMS‑Specific Interpretation

In the DRUMS framework, the BAO horizon corresponds to the phase‑coherent propagation length:

This directly ties the standard BAO scale to the evolution of the superfluid phase field. The coherence of the phase over cosmological distances is what allows the wavefront to propagate without dissipation.

Discrete Resonant Length Scales

Phase coherence over large scales enforces standing wave conditions. For modes that fit exactly within the acoustic horizon:

This quantization produces preferred clustering scales:

In the DRUMS picture, the BAO feature is not a single peak but a series of resonant scales arising from the quantized modes of the superfluid condensate.

Density Correlation Function

The two-point correlation function of matter density exhibits peaks at these resonant scales:

Constructive interference at scales equal to the quantized wavelengths enhances \(\xi(r)\) precisely at \(r = R_{\text{BAO}}, 2R_{\text{BAO}}, \dots\). This is exactly what is observed in galaxy redshift surveys.

Stability of the BAO Scale

Once the universe becomes neutral, the phase coherence freezes. The scale remains imprinted because:

• Phase coherence freezes after decoupling — the superfluid can no longer sustain propagating waves.
• Nonlinear gravitational evolution preserves large‑scale modes — the BAO feature is not washed out by structure formation.

Mathematically, for \(t > t_*\):

The frozen coherence length acts as a standard ruler that can be measured at different cosmic epochs.

Final Interpretation

Within the DRUMS framework, baryon acoustic oscillations arise naturally as:

• Phase-propagation horizons in a superfluid medium — the distance sound can travel is determined by the evolution of the coherent phase field.
• Standing wave resonances of the phase field — allowed modes are quantized by the condition that they fit within the causal horizon.
• Frozen coherence lengths after decoupling — the acoustic scale becomes a rigid feature imprinted on the matter distribution.

Thus, the observed BAO scale is a direct manifestation of the underlying phase dynamics and coherence structure of the cosmological superfluid. In standard cosmology, the BAO ruler is an input parameter derived from the sound horizon. In DRUMS, it is an output of the superfluid's quantum coherence properties — tied intimately to the same substrate that gives rise to gravity and the CMB anomalies.