arXiv:2601.04290v1 Announce Type: new
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 $E_6times E_6$ framework in which $SU(3)_Rrightarrow SU(2)_Rtimes U(1)_{Y’}rightarrow U(1)_{rm dem}$, 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.
Conclusions
The article presents a novel approach to combining General Relativity and MOND theory in a relativistic framework, utilizing a right-handed gauge sector within an $E_6times E_6$ framework. By recovering General Relativity in high-acceleration regimes and MOND behavior in low-acceleration regimes without introducing additional fields, the model provides a promising new perspective on gravitational interactions at different scales.
Future Roadmap
As readers consider the implications of this research, several challenges and opportunities lie ahead in the field of gravitational theory. Here is a roadmap outlining potential future directions:
- Experimental Validation: One of the key steps moving forward would be to test the predictions of this model against observational data, both at galactic scales where MOND is relevant and in high-precision tests where General Relativity holds.
- Theoretical Extensions: Exploring the consequences of this minimal relativistic completion of MOND could lead to a deeper understanding of the fundamental principles underlying gravity and its behavior at different acceleration regimes.
- Cosmological Implications: Investigating how this model extends to cosmological scales and its impact on the evolution of the universe could provide insights into the nature of dark matter, dark energy, and the overall dynamics of the cosmos.
- Computational Challenges: Implementing the equations derived from this framework in numerical simulations and calculations may pose computational challenges due to the complexity of the model, requiring innovative approaches for analysis.
- Interdisciplinary Collaboration: Bridging the gap between gravitational theory, particle physics, and cosmology could be facilitated by collaboration across disciplines, fostering new perspectives and collaborations to address the multifaceted nature of this research.
By following this roadmap and tackling these challenges head-on, researchers can unlock the full potential of this novel approach to relativistic MOND theory and pave the way for groundbreaking discoveries in the field of gravitational physics.