[Paper Review] Observational Evidence for Extra Dimensions from Dark Matter

Bo Qin, Ue‐Li Pen+1 more|arXiv (Cornell University)|Aug 26, 2005

Dark Matter and Cosmic Phenomena3 citations

TL;DR

This paper proposes that observational evidence for velocity-dependent dark matter self-interactions in galactic systems can be explained by the Arkani-Hamed–Dimopoulos–Dvali (ADD) scenario with three large extra dimensions. By linking the observed cross-section scaling to modified gravity at sub-nanometer scales (r⁻⁵ law), it derives a dark matter particle mass of ~3×10⁻¹⁶ proton mass, consistent with axions, and constrains the size of extra dimensions to ~1 nm.

ABSTRACT

Recent astronomical observations of systems of dark matter, which have been cited as providing possible support for self-interacting cold dark matter, may provide evidence for the extra dimensions predicted by superstring scenarios. We find that the properties of the required dark matter self-interaction are precisely the consequences of a world with 3 large extra dimensions of size \~1nm, where gravity follows the r^{-5} law at scales below ~1nm. From the cross sections measured for various dark matter systems, we also constrain the mass of dark matter particles to be m_x ~ 3*10^{-16} proton mass, consistent with the mass of axions.

Motivation & Objective

• To reconcile discrepancies between cold dark matter simulations and observations of dark matter halo profiles by proposing a physical mechanism for velocity-dependent self-interactions.
• To test whether the observed scaling of dark matter self-interaction cross sections with velocity dispersion can be explained by modified gravity in large extra dimensions.
• To constrain the number and size of large extra dimensions predicted by the ADD scenario using astrophysical data on dark matter systems.
• To link string theory predictions (large extra dimensions) with observable astrophysical phenomena, offering a falsifiable test of quantum gravity at sub-micron scales.

Proposed method

• Uses observational data on dark matter self-interaction cross sections from dwarf galaxies, low surface brightness galaxies, and galaxy clusters to derive a velocity-dependent scaling relation: σ_xx/m_x ≈ 4×10⁻²⁵ (100 km s⁻¹ / v) cm²/GeV.
• Applies classical and quantum mechanical scattering cross-section formulas for s-wave scattering in a 3+1+n dimensional gravity framework, with gravity following an r⁻⁵ law at scales below R.
• Derives the quantum mechanical cross section for identical bosons in n=3 large extra dimensions: σ_xx = 2π(αGm_x)¹ᐟ² / v, where α = Rⁿ.
• Combines the empirical cross-section scaling with the theoretical gravity model to solve for m_x and R, using the ADD relation R ∼ 10^(30/n − 17) cm.
• Validates the classical approximation by showing that quantum corrections (factor of 2 for bosons) do not alter the derived n=3 result.
• Tests consistency with current experimental limits on gravity at sub-mm scales, showing that deviations are expected at the nanometer scale (R ~ 10⁻⁷ cm).

Experimental results

Research questions

• RQ1 Can the observed velocity-dependent dark matter self-interaction cross section be explained by modified gravity in large extra dimensions?
• RQ2 What is the number of large extra dimensions (n) required to reproduce the observed scaling of dark matter cross sections with velocity dispersion?
• RQ3 What is the size R of the large extra dimensions implied by the observed self-interaction data?
• RQ4 What is the predicted mass of dark matter particles consistent with the derived extra-dimensional model?
• RQ5 Does the model remain consistent with current experimental limits on deviations from Newton’s inverse-square law?

Key findings

• The number of large extra dimensions is constrained to n = 3, based on matching the observed velocity-dependent self-interaction cross section to the r⁻⁵ gravity law.
• The size of the large extra dimensions is found to be R ∼ 10⁻⁷ cm (0.1 nm), where gravity deviates from Newtonian r⁻² to r⁻⁵ behavior.
• The dark matter particle mass is constrained to m_x ∼ 3×10⁻¹⁶ proton masses, placing it in the mass range expected for axions.
• The model explains the observed cross-section scaling without introducing new fine-tuned interactions, by attributing self-interactions to gravity in higher dimensions.
• The model predicts detectable deviations from Newton’s law at sub-nanometer scales, offering a falsifiable test of the ADD scenario.
• The derived cross section formula is consistent with both classical and quantum mechanical treatments, with corrections not altering the n=3 result.