A Relativistic MOND

TL;DR

This work presents a minimal relativistic MOND where General Relativity is exact in high-acceleration regimes while MOND emerges from a metric-only infrared deformation in the deep-MOND limit. The MOND scale is dynamically fixed by a de Sitter infrared vacuum through $a_0 = c^2/(\xi\ell_{\rm dS})$, and deep-MOND symmetry is implemented as a 3D conformal $SO(4,1)$ invariance in the static limit. Gravity is realized without extra propagating degrees of freedom via a Plebanski/MacDowell--Mansouri-inspired $SU(2)_R$ construction that yields an emergent tetrad and the Einstein--Hilbert action, with a healthy $U(1)_{\rm dem}$ sector remaining subleading. The framework yields clear observational handles, including robust MOND phenomenology tied to cosmological scales, no-slip lensing, and distinctive late-time structure growth, while highlighting open tasks to achieve a fully covariant completion and detailed cosmological perturbation theory.

Abstract

We present a minimal relativistic completion of MOND in which (i) General Relativity is recovered exactly in the high-acceleration regime, while (ii) the Bekenstein--Milgrom (AQUAL) equation emerges in the low-acceleration regime, without introducing additional propagating fields beyond those already present in a right-handed gauge sector. The construction is motivated by an $E_6\times E_6$ framework in which $SU(3)_R\rightarrow SU(2)_R\times U(1)_{Y'}\rightarrow U(1)_{\rm dem}$, leaving a healthy repulsive $U(1)_{\rm dem}$ interaction whose charge is the square-root mass label. Gravity itself arises from the $SU(2)_R$ connection via a Plebanski/MacDowell--Mansouri mechanism, yielding an emergent tetrad and the Einstein--Hilbert action. MOND is implemented by an infrared (IR) metric deformation $ΔS_{\rm IR}[g]$ that is UV-vanishing (so GR is recovered) while its deep-MOND/static limit is fixed by a symmetry principle: in three spatial dimensions, the deep-MOND action is conformally invariant with a 10-parameter group isomorphic to $SO(4,1)$ (the de Sitter group). The single MOND acceleration scale is set by a de Sitter radius selected dynamically in the IR, $a_0=c^2/(ξ\,\ell_{\rm dS})$ with $ξ={ O}(1)$ fixed by matching to the static limit. MOND resides in perturbations and quasistatic systems; the homogeneous FRW background is controlled by the IR vacuum kinematics rather than an ad hoc cosmological constant.