RESEARCH

Structural Cosmology. Work in progress, published in public.

Independent research by Charles W Rabico Jr — a pre-print brief and a funding proposal on whether gravitational time dilation can account for the galaxy rotation problem without dark matter.

Published in public, ahead of formal review. Independent work by Charles W Rabico Jr — no institutional affiliation, no peer-review stamp yet. If you think a step is wrong, that is exactly what this page is for.

The rotation problem, reframed

The galaxy rotation problem is usually resolved with unseen dark matter. This brief proposes the discrepancy may partly or wholly be an artifact of time.

Manuscript

Gravitational Time Dilation as an Alternative Explanation for the Galaxy Rotation Problem

Charles W Rabico Jr

Pre-print brief · submitted for scientific commentary · DOI pending

Stars at the outer edges of spiral galaxies orbit faster than Newtonian mechanics allows given the visible mass. The standard resolution is an undetected mass component. This brief argues that resolution assumes our time measurements across galactic structures are uniform — and they are not. A galaxy's core is dominated by a supermassive black hole where time slows dramatically; its sparse edge sits in far weaker curvature where time runs closer to flat-spacetime rates. Observed from an Earth-based frame, the core appears to tick slower and the edge faster. On this reading, the edge stars do not move faster — they are perceived through a different rate of time. The brief is deliberately qualitative: it proposes the mechanism and calls for quantifying time-dilation gradients from galactic centre to edge, simulating relativistic corrections on observed rotation curves, and comparing the result against dark-matter halo models.

Request the manuscript

Manuscript available on request.

The simulation work

Toward First-Principles Structural Cosmology — High-Resolution N-Body Simulations of Time-Dilation-Modified Baryonic Halos

Funding proposal · 2026

The proposal argues that the persistent failure of direct detection experiments to find WIMPs or axions justifies a pivot toward first-principles baryonic physics, and sets out to replace a fitted constant with a derived one. It treats gravitational time dilation as an active force that shapes mass distribution rather than a passive correction: in regions of deep curvature proper time runs slower, creating a feedback loop that traps cold baryonic remnants — rogue planets, primordial black holes, Population III remnants — in the slowest-running coordinates. Over 13.8 billion years this produces the modelled density enhancement in inner galactic regions.

The model

Central SMBH

point mass, extreme core curvature

Hernquist bulge

spherical mass distribution, no central singularity

Exponential disk

flattened visible midplane

NFW halo

baseline cuspy profile of Population III remnants before time-dilation modification

tau(r) = sqrt(1 + 2*Phi(r)/c^2)

rho_SC(r) = rho_NFW(r) * [1 + alpha(1 - tau(r))]

Because Phi is negative, tau < 1 — the local clock runs slow, and alpha acts as the informational coupling constant between matter and the local temporal gradient.

Pilot simulation results

Normalised RMS error across a three-galaxy test suite, comparing visible-only, standard NFW, and the time-dilation-modified model.

Galaxy	Total simulated mass (10^10 M_sun)	Visible only	Standard NFW	SC-modified	Relative improvement
Milky Way	38.004	0.2280	0.1372	0.1318	3.9%
Andromeda (M31)	63.030	0.2687	0.1961	0.1870	4.6%
NGC 2403	10.002	0.2673	0.1377	0.1352	1.8%

These figures reproduce from the public release — see The code below.

What this table is. The coupling constant alpha is a phenomenological fit at 500.0, not a derived value, so these figures measure fit quality — not predictive power. Deriving alpha from first principles is the entire point of the proposal, and the real test is whether the improvement survives that derivation. M31 shows the largest gain, which is what a deeper potential well predicts (core time dilation tau ≈ 0.999215, a +39.27% modelled density boost over the standard NFW cusp). The gains are modest. The work is unfinished. Both of those are stated here on purpose.

What would prove it wrong

The proposal commits to specific, falsifiable predictions. These are the tests that can kill the framework, stated in advance.

Nancy Grace Roman Space Telescope

Prediction: the Galactic Bulge Time-Domain Survey detects a significant excess of 50–150 short-timescale microlensing events (t_E under 1 day) per year — a rate 4x to 8x higher than standard stellar population models.

Vera C. Rubin Observatory (LSST)

Prediction: more than 10,000 isolated substellar objects detected in the solar neighbourhood, with a flattened radial topology that contradicts the steep drop-off a collisionless dark matter model requires.

The moving midpoint (spectroscopic)

Prediction: an intrinsic redshift in face-on galaxies that grows as inclination decreases. Standard models predict an H I 21cm emission peak at exactly 0.00 km/s for face-on galaxies; the framework predicts a shift that is only +12.04 km/s edge-on but grows to a systematic +74.92 km/s for face-on Milky Way-mass galaxies.

These are the numbers that can kill the framework, named before the data lands. That is what makes them worth measuring.

The code

The N-body work is public. The repository holds the simulation code; the Zenodo release is the citable, versioned snapshot of it.

Software release

Reference implementation — Structural Cosmology v0.1.0

Repository: github.com/crabico73/structural-cosmology
Version DOI: 10.5281/zenodo.21930235
Published: 14 August 2026
Licence: CC BY 4.0

Reference implementation of the Structural Cosmology equations for galaxy rotation curves and N-body structure formation.

What's in it

galaxy_rotation.py — core SC rotation-curve test across the Milky Way, M31 and NGC 2403
galaxy_combined.py — standard versus Population III versus observed comparison
galaxy_sc_roman.py — SC halo model with Roman/Rubin observatory predictions
sc_simulation_v2_paper.py — N-body simulation, PBH-seeded structure formation under time dilation
Combined output plots for all three galaxies plus a results.json

Reproducibility note from the release: observed velocity data is normalised for shape comparison, and the original un-normalised arrays for the results table are not included. The README and LICENSE are in the repository.

Cite it

crabico73 (2026). crabico73/structural-cosmology: Structural Cosmology v0.1.0 — Reference Implementation [Computer software]. Zenodo. https://doi.org/10.5281/zenodo.21930235

Open the repository

Cite, critique, correct

This work is published here to get more informed eyes on it than one person can provide, while formal review is pending. If you work in galactic dynamics, relativistic astrophysics or cosmology and you think a step is wrong, say so — that is what this page is for.

Read the author's note — My Best Guess →

Get notified when the papers and repository go public.

Author: Charles W Rabico Jr · VivaMarket