Infrared Spectral Gap in a Gluonic Dark Sector as the Origin of the Galactic Acceleration Scale

TL;DR

The paper proposes that the universal galactic acceleration scale originates from an infrared spectral gap in a gluonic dark sector, linked to the QCD trace anomaly and an Anti-de Sitter symmetry framework.

Contribution

It introduces a novel model connecting the galactic acceleration scale to a spectral gap in a gluonic dark sector, rooted in fundamental QCD and symmetry principles.

Findings

The acceleration scale matches the order of the observed galactic acceleration.

A spectral gap in the gluonic sector explains large-scale coherence in dark matter.

The model links the acceleration scale to a trace anomaly-induced infrared scale.

Abstract

The radial acceleration relation reveals a nearly universal acceleration scale of order $10^{-10}\,\mathrm{m\,s^{-2}}$ in galactic dynamics, whose origin remains unexplained within conventional cold dark matter scenarios. We explore the possibility that this scale is associated with an intrinsic infrared spectral property of the dark sector. Specifically, we hypothesize that a long-lived, color-neutral gluonic vacuum component surviving the post-inflationary expansion era organizes, at large distances, into a spectrally rigid lowest-weight structure. The microscopic seed for this infrared organization is provided by the QCD trace anomaly, which breaks classical scale invariance and, through dimensional transmutation, generates an intrinsic infrared scale in the gluonic sector. Within an effective representation-theoretic framework, Lorentz covariance together with a positive-energy lowest-weight unitary realization points naturally to the Anti-de Sitter algebra $\mathfrak{so}(2,3)$ as the simplest symmetry admitting a discrete tower of states with a representation-theoretically protected gap. The associated gap introduces a finite correlation length $r_{\texttt{c}}$ that controls the large-scale coherence of the dark sector. A self-gravitating condensate dominated by the lowest-weight mode then leads to a characteristic acceleration $g^{}_\star = G M_h / r_{\texttt{c}}^2$, naturally of the same order as the observed galactic acceleration scale, within standard Newtonian gravity. In this framework, the galactic acceleration scale is interpreted as the gravitational imprint of a trace-anomaly-seeded infrared spectral gap in a coherent gluonic dark sector, rather than as a consequence of modified gravity or of galaxy-by-galaxy formation histories.