Late-Time Coarsening of a Bistable Coherence Field in Expanding Cosmology: A Regime-Delimited Model Beyond the Boyanovsky–de Vega Large-N Domain
Year: 2026
Type: preprint
Abstract: We study the late-time coarsening dynamics of a scalar coherence field C(x,t) ∈ [0,1] governed by a bistable Allen–Cahn / Wright–Fisher reaction–diffusion equation in a spatially flat FRW background. This work does not dispute the Boyanovsky–de Vega scaling result for symmetry breaking in FRW cosmologies; it identifies a distinct late-time dissipative regime in which the observables, assumptions, and effective dynamics differ from those of the large-N quantum-field calculation. Through deterministic numerical integration on a periodic cubic lattice, we establish that the characteristic comoving length scale obeys the calibrated law ℓ²(t) = b + A·D_C·∫dt'/a²(t'), with a single effective prefactor A = 7.67 ± 0.20 consistent across four independent backgrounds (Minkowski, radiation, matter, de Sitter) with R² ≥ 0.996 in the pre-saturation window. The naïve dimensional estimate A = 2 is excluded; the exact prefactor is a measured property of the factorized Wright–Fisher kernel, not a universal constant. In de Sitter the accumulated comoving diffusion time saturates to 1/(2H), and we confirm numerically the corresponding double-freezing of the coarsening scale. The bistable front velocity supports the Aronson–Weinberger prediction in sign across all three FRW backgrounds and quantitatively in the best-resolved de Sitter case. A finite-noise robustness check (σ=0.1, radiation) shows the law survives in functional form with the prefactor renormalized downward ~20%. We delimit the domain of validity of this late-time dissipative description relative to the large-N quantum regime and identify the transition between the two (Regime II) as an explicit open problem.
Author: Cerezo, Arturo
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162124502