The non-linear clustering and void-centric density variation of the BMF framework imply that light propagation through the cosmic web should experience statistical lensing distortions inconsistent with CDM predictions.
Signature: Enhanced weak lensing shear in regions with fractal underdensities or across layered transitions.
Observable via:
LSST (Rubin Observatory): High-precision mapping of cosmic shear and gravitational lensing convergence maps.
Euclid & Roman Space Telescope: Sub-arcsecond resolution of lensed images can reveal small-scale perturbations not accounted for by smooth dark matter halos.
Challenge: Disentangling lensing noise due to baryonic feedback from fractal-induced lensing requires multi-scale correlation functions and machine learning classifiers trained on BMF simulations.
2. Redshift Drift and Hubble Layer Inference
The layer-dependent Hubble flow intrinsic to BMF cosmology predicts subtle deviations in cosmic redshift evolution, especially when comparing light from sources embedded in distinct expansion layers.
Signature: A non-linear time evolution of redshift from fixed astrophysical sources (e.g., Lyman-alpha forests, quasars).
Observable via:
ELT--HIRES (Extremely Large Telescope): Designed to detect redshift drift (Sandage--Loeb test) over decadal timescales.
Time-delay cosmography: Gravitationally lensed quasar systems where path-dependent expansion rates lead to multi-image drift asymmetries.
Challenge: Requires ultra-stable spectroscopic calibration over decades. Noise from peculiar velocities and intervening lensing structures must be modeled with BMF-inspired kinematics.
3. Gravitational Wave Echoes and Topological Layer Transitions
In the BMF framework, spacetime layer boundaries may act as discrete topological interfaces, influencing the propagation of gravitational waves (GWs) through modified dispersion or partial reflections.
Signature:
Gravitational wave echoes following black hole or neutron star mergers, with time delays correlated to layer crossing.
Anomalous dispersion relations or spectral "ringing" signatures inconsistent with General Relativity in vacuum.
Observable via:
LIGO/Virgo/KAGRA & LISA: Sensitive to high-frequency and long-duration GW tail structures.
Stacked analyses across events may reveal statistically significant late-time echo patterns.
Challenge: Echo detections are presently at the edge of instrument sensitivity and may be confounded by post-merger accretion dynamics. Requires new waveform templates generated from BMF's layered metric (see Section III.1).
4. Cosmic Microwave Background (CMB) Anisotropies and Phase Patterns
While BMF does not require inflation, it naturally predicts non-Gaussian anisotropies and hemispherical asymmetries in the CMB due to both layer transitions and fractal void topologies.
Signature:
Low-l multipole anomalies (e.g., quadrupole--octopole alignments),
Cold Spot reinterpretation as interference-induced feature across a void-layer boundary.
Observable via:
Planck (archival), LiteBIRD (upcoming),
Angular power spectrum residuals and bispectrum analysis to identify fractal or topological signatures.
Challenge: Distinguishing primordial topological interference from secondary anisotropies (e.g., ISW, SZ effects) requires forward-modeling the BMF imprint from early-time quantum blink fluctuations.
5. Large-Scale Structure Surveys and Layer Stratigraphy
The BMF model predicts non-Poissonian void distributions and radial-dependent clustering patterns due to expansion layer stratification.
Signature:
Radial void stacking statistics showing transition scales corresponding to Hubble layer boundaries,
Power spectrum "knees" deviating from CDM's linear prediction.
Observable via:
SKA & DESI: Galaxy redshift and 21-cm surveys providing 3D tomography of matter distribution.
Fractal dimension estimators: Derived from BMF simulations, allowing direct comparison with survey data.
Challenge: Requires volumetric completeness and deep redshift coverage. Anisotropic selection effects must be carefully controlled.
6. Other Prospective Observables
Final Note on Experimental Philosophy
