Emergent Teleparallelism from a Spontaneously Broken (A)dS Gauge Symmetry

Abstract

We present a pre-geometric construction of the Teleparallel Equivalent of General Relativity (TEGR) wherein gravity emerges from the spontaneous breaking of a global (A)dS gauge symmetry to the Lorentz subgroup. Starting from a bare manifold devoid of any metric or tetrad structure, we introduce a scalar multiplet transforming under the global SO(1, 4) (or SO(2, 3)) group. The theory is subsequently promoted to a local gauge-invariant form by introducing a connection and covariant derivatives. The tetrads and spin connections emerge from the components of the gauge connections after spontaneous symmetry breaking. We construct three non-linear invariants from the scalar field and its derivatives that, upon symmetry breaking, reconstruct precisely the torsion scalar of TEGR. The resulting action is free from Ostrogradsky instabilities due to the antisymmetric structure of the kinetic terms. The symmetry-breaking potential, taken as a general functional of the scalar field, generates both the Planck scale and the cosmological constant dynamically. We discuss the implications of our framework for early-universe cosmology, including the possibility that the Higgs field plays the role of the inflaton or constitutes superheavy dark matter produced non-thermally during inflation. The constant part of the potential after symmetry breaking provides a natural source for dark energy.