The Critical Hypersurface as a Geometric Origin of Nonsingular Cosmic Expansion

We propose a geometrically motivated framework in which the large-scale evolution of the Universe is described by a coherent multidimensional wavefunction possessing a preferred direction of propagation. Within this formulation, the scalar envelope of the wavefunction defines a critical hypersurface whose temporal evolution provides an effective geometric description of cosmic expansion. The resulting picture naturally incorporates an arrow of time, large-scale homogeneity, and a nonsingular expansion history, without invoking an inflationary phase, a cosmological constant, or an initial singularity. The critical hypersurface takes the form of a three-dimensional sphere whose radius plays the role of a cosmological scale factor. Its evolution leads to a time-dependent expansion rate with a positive but gradually decreasing acceleration. The associated density evolution follows a well-defined scaling law that is consistent with the standard stress–energy continuity equation and corresponds to an effective equation-of-state parameter w = -1/3. As a consequence, the total mass–energy contained within the expanding hypersurface increases with time in a manner that remains fully compatible with the continuity relation. Analytical estimates derived from the model yield values for the present expansion rate and mean density that are in close agreement with current observational constraints. Within this geometric interpretation, the gravitational constant emerges as an invariant global potential associated with the critical hypersurface, linking the conserved properties of the wavefunction to observable gravitational coupling. The framework therefore provides a self-consistent, effective description in which cosmic expansion and gravitational dynamics arise from the geometry of a universal wavefunction, suggesting a deep connection between quantum structure, spacetime geometry, and cosmological evolution.