Horizon-Level Information Erasure as an Emergent Running Vacuum: Cosmological Implications for Structure Growth and the ISW Effect

We propose a physically motivated link between horizon thermodynamics, Landauer’s principle and a small running vacuum component in cosmology. Interpreting black holes and cosmological horizons as physically active loci of information reclamation (“ontological erasure”), we show that the thermodynamic cost of erasing horizon-encoded bits naturally produces a contribution to the vacuum energy proportional to . We present a phenomenological and self-consistent realization of this idea as a small running-vacuum model (RVM)-type term with whose microphysical origin is traced to an horizon–Landauer mechanism. We derive background dynamics, linear perturbation equations, and compute leading-order consequences for structure growth (growth index and ) and the late-time Integrated Sachs–Wolfe (ISW) signature. We identify observationally-falsifiable ranges of (order ) that mildly reduce the tension while preserving agreement with background data and CMB constraints, and we outline robust tests and numerical strategies for confronting the model with current and upcoming data.