• Accepted Paper

Quantum gravitational mechanism for isotropization of de Sitter cosmologies

Stephon Alexander, Bruno Alexandre, Daine L. Danielson, and David N. Spergel

Phys. Rev. D - Accepted 2 November, 2026

DOI: https://doi.org/10.1103/nd42-szrf

Abstract

The observable cosmos exhibits a remarkable degree of isotropy and plausibly began in a nearly isotropic initial state. The origins of this isotropy constitute a longstanding puzzle, and the properties of the Lorentzian Chern-Simons-Kodama (CSK) functional can provide an understanding of this initial state. In gravity with a positive cosmological constant, the Chern-Simons-Kodama wavefunctional is an exact solution of the quantum gravitational constraints. We suggest that the normalizability and other issues with this functional, which arise when interpreted as a proper state of quantum gravity, instead point to an embedding into a larger quantum gravitational completion and a distinct choice of integration cycle. Together these recast the CSK functional as a sphaleron-like saddle with observationally desirable properties. By perturbing around the dominant de Sitter saddle of the wavefunctional with appropriate quantum gravitational boundary conditions and integration contour, we find that for a closed universe the system probabilistically and dynamically favors spatial isotropy, while all anisotropic modes acquire positive quadratic curvature and are Gaussian-suppressed. The decay of this sphaleron-like configuration therefore proceeds along an isotropic channel, providing an intrinsic quantum-gravitational mechanism for isotropization. Beyond minisuperspace, the mechanism depends on the chosen no-boundary transverse contour, not the bare CSK functional alone; a fully nonperturbative contour completion remains open. A preliminary investigation suggests the effect may be robust under the inclusion of a slow-roll inflaton, and we find no analogous isotropic saddle exists for spatially flat or hyperbolic geometries. Taken together, these results recast the Lorentzian CSK functional as a sphaleron-like saddle that locally favors an approximately isotropic de Sitter background for inflation. Beyond this phenomenological study, we further suggest that the CSK functional can be understood as a boundary functional for a class of anomaly-free objects, including a complexified generalization of the Hartle-Hawking state.

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