Transport of Compensated Baryon-Asymmetry Domains in an Expanding Universe with Exact Spherical Diffusion and a Conditional Scalar-Field Test

Abstract This paper examines how diffusion changes a finite, globally compensated baryon-asymmetry profile in an expanding, spatially flat Friedmann-Lema\^{i}tre-Robertson-Walker universe. Coupled baryon and antibaryon balance equations are reduced to an equation for the signed asymmetry, and the conditions for conservation of its spatial integral are stated. Using the accumulated comoving diffusivity, we derive the exact three-dimensional heat-kernel response for a spherical positive core surrounded by an oppositely signed shell whose amplitude is fixed by volume compensation. The resulting central-contrast function gives a 95\% retention threshold that depends on the shell-to-core radius ratio. For a radius ratio of two, the dimensionless diffusion time must satisfy $I_D/R_c^2\leq0.06164$, compared with $0.13016$ for a planar step. At late times, cancellation of the monopole moment leads to a central decay proportional to $u^{-5/2}$. A separate conditional scalar-field benchmark, normalised to the baryon-to-photon ratio, gives $m_\phi=(5.073\pm0.016)\times10^{-16}$ GeV for the stated parameters.