A Relativistic Extension of the R-layer Theory Unified Origin of MOND and Cosmological Acceleration

Abstract

We present a fully relativistic formulation of the R-layer theory, in which the observed MOND phenomenology arises from the elastic response of an external layer surrounding the spacetime. The R-layer is described by a scalar displacement field phi with inertial coefficient Z, bending rigidity K, potential V(phi), and baryonic coupling alpha. We construct the covariant action, derive the field equations and stress-energy tensor, and analyze the resulting dynamics in both cosmological and static backgrounds. In a Friedmann–Robertson–Walker universe, the displacement field experiences a Hubble friction term proportional to 3H times the time derivative of phi, effectively enhancing the inertial coefficient to Z_eff approximately equal to Z multiplied by H. In static, spherically symmetric systems, the competition between the Z term and the K term yields a transition between Newtonian and MOND regimes, with a characteristic acceleration scale a0 approximately equal to (Z_eff divided by K), which is approximately (Z multiplied by H divided by K). This provides a dynamical explanation for the empirical relation a0 approximately equal to H0. The theory naturally reproduces the baryonic Tully–Fisher relation, flat rotation curves, and the external field effect, while offering a unified geometric interpretation of galactic dynamics and cosmological acceleration. We discuss the relation to other relativistic MOND theories, the physical interpretation of the R-layer, and possible extensions to black-hole and horizon-scale physics.

Keywords