The Topological Multiverse as the Self-Consistent Extension of Everettian QM to Quantum Gravity

Abstract

The ``fine-tuning" of the fundamental constants, from the cosmological constant to the gauge structure of the Standard Model, suggests that our universe inhabits a rare, life-permitting island within a vast landscape of theoretical possibilities. We argue that this landscape arises as a self-consistent extension of Everettian quantum mechanics, once the Wheeler--DeWitt path integral is allowed to sum over admissible topologies rather than being restricted to a single background. Enlarging the DeWitt sum of geometries to include all smooth manifolds supporting causal dynamics promotes the dimensionality, gauge groups, and coupling constants from fixed background inputs to dynamical variables of the sum. The functional integral requires a differentiable manifold, so the geometry terminates where curvature reaches the Planck scale and $W^{2,2}$ regularity fails; the universe originates at this boundary $\mathcal{B}_Q$ as a smooth manifold, rather than from a singularity or a pre-geometric foam. At $\mathcal{B}_Q$, the integral generates a coherent superposition of distinct topologies that branch into disjoint U-sectors, each governed by its own effective field theory, with inter-sector transitions dynamically frozen shortly after nucleation. We further identify a thermodynamic selection rule governing nucleation: the Gibbons--Hawking weight, with the free gravitational field's contribution expressed through the Bel--Robinson super-energy, favors hot, homogeneous, low-Weyl seeds. This furnishes a dynamical realization of Penrose's Weyl curvature hypothesis and supplies Big-Bang-like initial conditions without a separate inflationary potential. The topological multiverse is, in this view, not imposed but implicit in Everettian quantum mechanics applied to a gravitational sum over geometries.