We identify the complete set of fundamental building blocks for a 4D pregeometric theory of gravity. Based on a gauge theory of $SO(1,4)$ or $SO(2,3)$ coupled to a Higgs-like field under the rigid constraint of general covariance in the unbroken phase, these building blocks (${\mathcal{L}}_{\mathrm{MM}}$, ${\mathcal{L}}_{\mathrm{W}}$, ${\mathcal{L}}_J$, ${\mathcal{L}}_{\theta }$, and ${\mathcal{L}}_{\vartheta }$) constitute the minimal generating set of independent field monomials from which any pregeometric action, including arbitrary functionals thereof, can be constructed. While the most general pregeometric theory can extend beyond linear combinations, these five irreducible invariants serve as the “atomic” constituents of all possible pregeometric dynamics. Upon spontaneous symmetry breaking, they collectively generate an emergent gravitational theory consisting of the Einstein-Hilbert action, the cosmological constant term, and all 4D topological invariants: the Gauss-Bonnet, Pontryagin, Holst, and Nieh-Yan terms. The unification of gravity’s dynamical and topological sectors from a common pregeometric source represents the central result of this work. We also uncover a seesaw mechanism linking the Planck mass and the cosmological constant, as well as several novel relations for the coupling constants of the topological sector, inclusive of the Barbero-Immirzi parameter. This framework establishes the pregeometric foundations from which all aspects of gravitation can dynamically emerge, providing a unified starting point for quantum gravity, dark energy phenomenology, and the study of topological phases in gravitational theories.

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• Alternative gravity theories
• Gravitation
• Quantum gravity