Gauge-invariant non-universal scalar couplings in teleparallel gravity

Abstract

We develop a gauge-invariant teleparallel framework in which the universality of the gravitational coupling is relaxed for a scalar field, while the gravitational sector retains the form of the teleparallel equivalent of General Relativity. The non-universal interaction is encoded in a scalar-sector tetrad whose coupling to the universal translational gauge potential is controlled by a field-dependent gravitational charge. A Stückelberg completion preserves local translational gauge invariance, and we derive the gravitational, scalar-field, and Stückelberg equations, together with the antisymmetric constraint and their consistency relations. As a first application, we investigate homogeneous and isotropic cosmology, where the Stückelberg constraint provides a first integral governing the evolution of the non-universal coupling. In the kination-dominated regime, the standard stiff-fluid behavior is recovered asymptotically, whereas in the potential-dominated regime, accelerated expansion requires additional conditions beyond potential domination. We identify compatible expanding solutions in which departures from universality are dynamically suppressed, including examples approaching power-law inflation or asymptotically de Sitter expansion. Including a universally coupled perfect fluid and a constant scalar potential, we obtain a late-time solution exhibiting a subdominant matter-like contribution to the background Friedmann equation and an asymptotic de Sitter limit. These results provide a gauge-theoretic realization of non-universal scalar couplings and highlight their potential implications for early- and late-time cosmology.