A Relativistic MOND

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 $\Delta S_{\rm IR}[g]$ 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, $a_0=c^2/(\xi\,\ell_{\rm dS})$ with $\xi={ O}(1)$ 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.