[Paper Review] Attractive and Repulsive Gravity

Philip D. Mannheim|arXiv (Cornell University)|Jan 6, 2000

Cosmology and Gravitation Theories3 references4 citations

TL;DR

This paper argues that gravity may be repulsive on cosmological distance scales, challenging the assumption that gravity is universally attractive. Using conformal gravity, the author shows that a repulsive component naturally resolves multiple cosmological problems—such as flatness, horizon, dark matter, cosmic acceleration, and the cosmological constant problem—by introducing a universal acceleration scale that aligns with observed galactic dynamics.

ABSTRACT

We discuss the circumstances under which gravity might be repulsive rather than attractive. In particular we show why our standard solar system distance scale gravitational intuition need not be a reliable guide to the behavior of gravitational phenomena on altogether larger distance scales such as cosmological, and argue that in fact gravity actually gets to act repulsively on such distance scales. With such repulsion a variety of current cosmological problems (the flatness, horizon, dark matter, universe age, cosmic acceleration and cosmological constant problems) are then all naturally resolved.

Motivation & Objective

• To challenge the assumption that gravity is universally attractive, especially beyond solar system scales.
• To address the failure of standard general relativity to explain galactic rotation curves without invoking dark matter.
• To propose that cosmological observations suggest a non-zero spatial curvature, implying gravity can be repulsive on large scales.
• To demonstrate that conformal gravity naturally produces a universal acceleration scale matching observational data.
• To argue that the standard extrapolation of Newtonian and Einstein gravity may be fundamentally flawed due to overreliance on weak-field solar system data.

Proposed method

• Formulates a conformal gravity theory that extends general relativity with local Weyl invariance, allowing for a repulsive gravitational component.
• Derives a modified gravitational potential that includes a term proportional to $ r $, leading to repulsive effects at large distances.
• Uses the conformal gravity action to derive field equations that predict a universal acceleration scale $ a_0 \sim 10^{-8} \, \text{cm/s}^2 $, matching observed galactic dynamics.
• Compares predictions of conformal gravity with observational data on galaxy rotation curves and mass discrepancy profiles.
• Analyzes the role of spatial curvature in generating a cosmological scale, contrasting flat standard cosmology with conformal gravity's non-zero curvature.
• Evaluates the cosmological constant problem and cosmic acceleration within the conformal gravity framework, showing natural resolution without fine-tuning.

Experimental results

Research questions

• RQ1 Under what conditions can gravity be repulsive rather than purely attractive?
• RQ2 Can the observed mass discrepancies in galaxies be explained without invoking dark matter?
• RQ3 Does the existence of a universal acceleration scale in galactic dynamics imply a fundamental modification of gravity?
• RQ4 Can conformal gravity resolve the flatness, horizon, and cosmological constant problems simultaneously?
• RQ5 Is the standard extrapolation of Newtonian and Einstein gravity to cosmological scales physically justified?

Key findings

• Conformal gravity predicts a repulsive gravitational component at large distances, arising from a $ r $-dependent term in the potential, which naturally explains flat rotation curves.
• The theory introduces a universal acceleration scale $ a_0 \sim 10^{-8} \, \text{cm/s}^2 $, matching the observed threshold for mass discrepancy in galaxies.
• The observed mass discrepancy in galaxies ($ M_{\text{dyn}}/M_{\text{lum}} > 1 $) systematically appears when orbital accelerations fall below $ 10^{-8} \, \text{cm/s}^2 $, consistent with conformal gravity predictions.
• The theory resolves the cosmological constant problem by naturally generating a small effective cosmological constant without fine-tuning.
• The flatness and horizon problems are resolved due to the non-zero spatial curvature inherent in conformal gravity, which provides a natural scale for structure formation.
• The model avoids the need for dark matter by deriving galactic rotation curves directly from luminous matter and the conformal gravity potential, without free parameters per halo.