Cosmic Acceleration Without Dark Energy: A MIDH-Based Toy Model of Scale-Factor-Dependent Inertia v2: Extended to Non-Constant μ(a) in Light of DESI DR2

This paper presents a toy model inspired by the Mutual Information Density Hypothesis (MIDH) and the informational-inertia conjecture introduced in earlier work. If inertia is tied to correlation-reconfiguration cost, and if this cost decreases as cosmological expansion dilutes large-scale mutual information density, then the Friedmann acceleration equation naturally acquires an effective positive term that mimics the behavior of dark energy—without invoking a cosmological constant or any exotic vacuum fluid.
In its simplest form (v1, November 2025), the model assumes a scale-factor-dependent interface capacity μ(a) = 1/(f·a³), yielding an emergent constant term mathematically indistinguishable from Λ in the ΛCDM model. This reproduces the late-time sign flip of the acceleration parameter, matter-dominated deceleration at early times, and the transition at z ≈ 0.6. No new fields, particles, or vacuum energy are required.
In light of results from the Dark Energy Spectroscopic Instrument (DESI DR2, March 2025) and the Dark Energy Survey (DES), which provide mounting evidence that dark energy may not be constant but evolving—stronger in the past, weakening at late times—this paper extends the model (v2, March 2026). By generalizing μ(a) to include an epoch-dependent correction ε(a) capturing non-uniform correlation dilution driven by the competition between structure formation and cosmological expansion, the framework yields an effective dark energy density ρ_DE(a) and equation of state w(a) ≠ −1, consistent with the DESI signal. A constant Λ was always the idealized limit; evolving dark energy is the generic case. If the DESI signal fades with improved systematics, the constant case remains valid. If it holds, the MIDH framework offered the structural explanation before the data arrived.