Horizon Thermodynamics and Late-Time Evolving Dark Energy

Recent observations of large-scale structure hint that the dark energy equation of state maydeviate from a strict cosmological constant at late times. We propose a minimal, physicallytransparent framework in which the late-time dark energy dynamics are linked to the thermodynamics of the apparent horizon in a spatially flat FLRW spacetime. Identifying the horizonentropy SH ∝ H−2 and temperature TH ∝ H, we introduce a single dimensionless coupling ϵthat governs departures from ΛCDM. In the ϵ → 0 limit one recovers exactly w = −1, while forϵ ̸ =0 the effective dark energy equation of state evolves according to˙wde(t) = −1 − 2ϵHH2 .We derive a closed algebraic expression for wde(a) in terms of the fractional densities, map ourmodel onto the usual CPL (w0,wa) parameters, and compute predictions for H(z), distance measures, and linear growth in General Relativity. Three falsifiable signatures emerge—correlatedresiduals in BAO/SN distances, a linked shift in fσ8(z), and a distinctive ISW/lensing-potentialtrend. We also provide a fully reproducible numerical recipe for implementing the model.