Gravity from Pre-geometry

Abstract

The gravitational interaction, as described by the Einstein-Cartan theory, is shown to emerge as the by-product of the spontaneous symmetry breaking of a gauge symmetry in a pre-geometric four-dimensional spacetime. Starting from a formulation à la Yang-Mills on an SO(1,4) or SO(3,2) principal bundle and not accounting for a spacetime metric, the Einstein-Hilbert action is recovered after the identification of the effective spacetime metric and spin connection for the residual SO(1,3) gauge symmetry of the spontaneously broken phase - i.e. the stabiliser of the SO(1,4) or SO(3,2) gauge group. Thus, the two fundamental tenets of General Relativity, i.e. diffeomorphism invariance and the equivalence principle, can arise from a more fundamental gauge principle. The two mass parameters that characterise Einstein gravity, namely the Planck mass and the cosmological constant, are likewise shown to be emergent, with the correct sign for the cosmological constant depending on whether the fundamental gauge group is taken to be either the de Sitter or the anti-de Sitter group. The phase transition from the unbroken to the spontaneously broken phase is expected to happen close to the Planck temperature. This is conjectured to be dynamically driven by a scalar field that implements a Higgs mechanism, hence providing mass to new particles, with consequences for cosmology and high-energy physics. The couplings of gravity to matter are discussed after drawing up a dictionary that interconnects pre-geometric and effective geometric quantities. In the unbroken phase where the fundamental gauge symmetry is restored, the theory is potentially power-counting renormalisable without matter, offering a novel path towards a UV completion of Einstein gravity.

Version accepted in CQG

References in corpus (8)

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Cited by in corpus (6)

• Hamiltonian Analysis of Pre-geometric Gravity
• Pre-geometric Einstein-Cartan Field Equations and Emergent Cosmology
• $\mathcal{H}$olographic $\mathcal{N}$aturalness and Pre-Geometric Gravity
• $\mathcal{H}$olographic $\mathcal{N}$aturalness and Information See-Saw Mechanism for Neutrinos
• Minisuperspace Cosmology in Extended Geometric Trinity of Gravity
• Emergence of Gravity's Dynamical and Topological Sectors from Pre-geometry