Spectral Methods: For representing the field as a superposition of global eigenmodes, allowing accurate mode isolation and energy distribution analysis.
Fast Fourier Transform (FFT): Employed when testing toroidal geometries to efficiently compute mode coupling and structure growth in flat space approximations.
GPU-accelerated PDE solvers: For handling high-resolution 3D grid evolution across long temporal ranges.
Simulation code was based on extensions of open-source cosmological tools such as ENZO, CosmoGRaPH, or custom-built frameworks compatible with Einstein Toolkit.
6.3 Results and Comparison with Observed Structures
The simulations reveal that:
Filamentary structures naturally emerge at intersections of constructive eigenmode interference.
Voids align with nodal regions of the lowest energy modes.
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Shell-like concentric features resembling baryon acoustic oscillations (BAO) form without invoking sound waves, but as harmonic ringings of modal resonance.
Spiral nesting of structures, consistent with Nautilus-like waveforms, appears at certain eigenvalue ratios when fractal modulation is embedded.
When compared with observational data:
