[Paper Review] Gravitational effects of the faraway matter on the rotation curves of spiral galaxies

A. Carati|arXiv (Cornell University)|Nov 24, 2011

Scientific Research and Discoveries3 references3 citations

TL;DR

This paper proposes that the gravitational influence of distant, faraway matter—accounting for retarded potentials and spatial correlations—can explain the flat rotation curves of spiral galaxies without invoking dark matter. By modeling the long-range, decorrelated gravitational force from the cosmic large-scale structure, the author fits observed rotation curves of four galaxies (NGC 3198, NGC 2403, UGC 2885, NGC 4725) with reasonable luminosity–mass ratios, demonstrating that a force of order 0.2cH₀ per unit mass arises from distant matter and dominates at galactic scales.

ABSTRACT

It was recently shown that in cosmology the gravitational action of faraway matter has quite relevant effects, if retardation of the forces and discreteness of matter (with its spatial correlation) are taken into account. Indeed, far matter was found to exert, on a test particle, a force per unit mass of the order of 0.2 cH0 . It is shown here that such a force can account for the observed rotational velocity curves in spiral galaxies, if the force is assumed to be decorrelated beyond a sufficiently large distance, of the order of 1 kpc. In particular we fit the rotation curves of the galaxies NGC 3198, NGC 2403, UGC 2885 and NGC 4725 without any need of introducing dark matter at all. Two cases of galaxies presenting faster than keplerian decay are also considered.

Motivation & Objective

• To investigate whether the gravitational action of distant matter—accounting for retardation and spatial correlation—can explain the observed flat rotation curves of spiral galaxies.
• To challenge the standard assumption that faraway galaxies can be neglected in galactic dynamics, especially given their non-uniform, fractal-like distribution.
• To demonstrate that a long-range, decorrelated gravitational force from distant matter can reproduce observed rotation curves without requiring dark matter.
• To provide a phenomenological model that accounts for the anomalous velocity profiles in galaxies using only standard general relativity and observed cosmological parameters.

Proposed method

• Model the universe as a collection of discrete, point-like galaxies with velocities following Hubble's law, assuming a time-independent Hubble constant H₀.
• Use linearized Einstein field equations with a perturbative energy-momentum tensor derived from the motion of distant galaxies, treating the metric as a small perturbation of Minkowski space.
• Apply the Wiener–Khinchin theorem to relate the spatial correlation of the gravitational field to the correlation of its derivatives, assuming an exponential decay length scale l.
• Introduce a decorrelation length of ~1 kpc beyond which the gravitational field from distant matter becomes uncorrelated, enabling a net long-range force.
• Compute the effective gravitational force per unit mass as 0.2cH₀, derived from statistical averaging over the spatial distribution of distant galaxies.
• Fit the resulting force law to observed rotation curves of four spiral galaxies, adjusting the luminosity–mass ratio to match data without dark matter.

Experimental results

Research questions

• RQ1 Can the gravitational influence of faraway matter—accounting for retardation and spatial correlation—explain the flat rotation curves of spiral galaxies without invoking dark matter?
• RQ2 What is the magnitude and spatial scale of the net gravitational force exerted by distant matter on a test particle in a galaxy?
• RQ3 How does the assumption of decorrelation beyond ~1 kpc affect the effective gravitational potential and rotation curve shape?
• RQ4 Can this model reproduce the rotation curves of galaxies with diverse masses and sizes using only standard gravitational theory and observed cosmological parameters?
• RQ5 Why is this effect negligible in the solar system but dominant in galaxies and clusters?

Key findings

• The gravitational force from faraway matter exerts a net acceleration of approximately 0.2cH₀ per unit mass on a test particle, arising from retardation and spatial correlation effects.
• This force becomes significant at galactic scales (~kpc) and dominates over local gravitational forces, explaining the flat rotation curves.
• The model successfully fits the rotation curves of four spiral galaxies—NGC 3198, NGC 2403, UGC 2885, and NGC 4725—without requiring dark matter.
• The luminosity–mass ratios derived from the fits are physically reasonable, indicating consistency with observed stellar masses.
• The model accounts for galaxies with faster-than-Keplerian decay, suggesting the long-range force can explain deviations from Newtonian expectations.
• The decorrelation length of ~1 kpc is critical: below this scale, the force is suppressed, while beyond it, the force becomes coherent and dominant.