Dynamic Holographic Dark Energy with Information Saturation

We propose a cosmological framework in which dark energy emerges from the dynamics of information constrained by holographic bounds [3, 4]. Instead of identifyinginformation with horizon entropy, we introduce a time-dependent saturation factorξ(t), such that the total information content is I(t) = ξ(t)SBH(t). Dark energydensity is postulated to be proportional to the time derivative of this information,ρde ∝ ˙I. This leads to a modi ed Friedmann equation with nonlinear terms in theHubble parameter and its derivative. The model ensures positive dark energy density, reproduces ΛCDM at early times [9], and predicts scale-dependent dynamics.Analytical formulation, limiting regimes, and observational signatures are presented;numerical analysis is illustrated for representative parameters