Relational Wave Cosmology: An Exact Self-Interacting Vacuum Solution for the Rotation Curves and Virial Masses of Disk Galaxies
- 1Independent University, Bangladesh
Abstract
(English)
We derive the equilibrium rotation curve of disk galaxies from the Relational Wave Cosmology (COR), a field theory in which space-time geometry and gravitational phenomena emerge from the dynamics of a complex scalar field with intrinsic memory. Under the assumptions of static spherical symmetry, the field equation reduces to the Lane--Emden equation of index n=5, whose analytic solution is the Schuster--Emden profile.
Through the core hypothesis of relational densification (rho_r proportional to |Phi|^2), this amplitude profile produces a circular velocity that rises linearly in the inner region and asymptotically approaches a constant value — a flat rotation curve. We show that the resulting velocity function is virtually identical to the phenomenological CVR-K model, fitting 115 SPARC disk galaxies with a decisive AIC/BIC preference over the standard NFW halo. Furthermore, by imposing a virial boundary condition tied to the cosmic critical density, the COR predicts halo virial masses M_200 and an internal Tully--Fisher scaling. The COR thus provides a first-principles explanation of galactic dynamics without invoking particulate dark matter.
Bundle Contents (Reproducibility):
- LaTeX manuscript (main.tex)
- SPARC dataset files and MRT/TXT tables
- Python analysis pipelines (benchmark_cor_native.py, calculate_virial_cor.py, plot_virial_scaling.py)
- Diagnostic plots and README instructions
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BibTeX
@misc{soares2026relational,
title = {{Relational Wave Cosmology: An Exact Self-Interacting Vacuum Solution for the Rotation Curves and Virial Masses of Disk Galaxies}},
author = {Francisco Wellington Gomes Soares},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23454554},
url = {https://zenodo.org/records/23454554},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Relational Wave Cosmology: An Exact Self-Interacting Vacuum Solution for the Rotation Curves and Virial Masses of Disk Galaxies
AU - Francisco Wellington Gomes Soares
PY - 2026
DA - 2026/10/18
PB - Zenodo
DO - 10.5281/zenodo.23454554
UR - https://zenodo.org/records/23454554
AB - (English) We derive the equilibrium rotation curve of disk galaxies from the Relational Wave Cosmology (COR), a field theory in which space-time geometry and gravitational phenomena emerge from the dynamics of a complex scalar field with intrinsic memory. Under the assumptions of static spherical symmetry, the field equation reduces to the Lane--Emden equation of index n=5, whose analytic solution is the Schuster--Emden profile. Through the core hypothesis of relational densification (rho_r proportional to |Phi|^2), this amplitude profile produces a circular velocity that rises linearly in the inner region and asymptotically approaches a constant value — a flat rotation curve. We show that the resulting velocity function is virtually identical to the phenomenological CVR-K model, fitting 115 SPARC disk galaxies with a decisive AIC/BIC preference over the standard NFW halo. Furthermore, by imposing a virial boundary condition tied to the cosmic critical density, the COR predicts halo virial masses M_200 and an internal Tully--Fisher scaling. The COR thus provides a first-principles explanation of galactic dynamics without invoking particulate dark matter. Bundle Contents (Reproducibility): - LaTeX manuscript (main.tex) - SPARC dataset files and MRT/TXT tables - Python analysis pipelines (benchmark_cor_native.py, calculate_virial_cor.py, plot_virial_scaling.py) - Diagnostic plots and README instructions
ER -