MMS-A16 - Background Cosmology with Delayed Entropy Production

This paper represents an earlier stage in the development of the Entropic Spacetime Field (ESF) framework. The current reference implementation is presented in MMS-A19: The Entropic Spacetime Field: A Canonical Wave Framework for Cosmic Structure Formation 10.5281/zenodo.21433778, which supersedes the mathematical formulation described here while retaining a number of the underlying physical concepts. The Entropic Spacetime Field (ESF) is a phenomenological framework in which spacetime is treated as a thermodynamic medium whose large-scale behaviour emerges from entropy production, transport, and saturation within a persistent ripplefield microstructure. In ESF, effects commonly attributed to dark matter and dark energy arise not from new particles or vacuum energy, but from the delayed dynamical response of spacetime geometry to ordinary baryonic matter as cosmic structure and electromagnetic interactions develop. This paper presents a toy background cosmology for ESF in which entropy production is suppressed at high redshift and activated gradually at later times using a smooth sigmoid factor. The resulting model preserves standard early-universe behaviour, exhibits modest intermediate-redshift deviations in the Hubble expansion rate (∼1–4% at z ≈ 3–8) and saturates naturally to late-time acceleration with an effective equation of state approaching w ≈ −1. Three canonical parameter sets are introduced to illustrate different entropy activation timings, all of which remain consistent with early-universe constraints. In addition, a set of falsifiable predictions is compiled, identifying specific observational regimes where ESF can be distinguished from ΛCDM. A concrete, near-term observational test is proposed: an excess weak-lensing convergence signal at the edges of non-virialised cosmic web filaments, decoupled from baryonic gas tracers, arising from persistent geometric memory in the ripplefield. This test is feasible using existing public weak-lensing and filament catalogue data. The purpose of this paper is not to fit cosmological data, but to establish a stable, testable background foundation for ESF and to define clear empirical pathways by which the framework may be supported or falsified.