Time as Phase Flow II: Information-Induced Temporal Inertia and Cosmological Perturbations in Information-Geometric Spacetime

We extend the Information-Geometric Spacetime framework from background evolution to the regime of linear perturbations to address cosmological tensions in a unified manner. Building on the “Time as Phase Flow” hypothesis, we propose that local matter overdensities perturb the entanglement structure of quantum fields across horizons, inducing a local modification of temporal flow interpreted as “information-induced temporal inertia” or information friction (Γinfo). By adopting a minimal closure relation where entanglement fluctuations are proportional to matter density contrast, governed by a coupling parameter α ≈ β ≈ 0.18 consistent with our previous background analysis, we derive the modified growth equation for matter perturbations. The model naturally predicts a systematic suppression of latetime structure growth, yielding fσ8 values consistent with Redshift-Space Distortion (RSD) and weak lensing measurements without modifying Einstein’s field equations or invoking afifth force. These results provide a unified, information-theoretic resolution to both the H0 and σ8 tensions through a single dynamical mechanism.