Running Planck Mass as a Minimal Extension of ΛCDM

We submit for consideration our manuscript entitled“Running Planck Mass as a Minimal Extension of ΛCDM”. The work proposes a minimal late-time modification of the gravitational sector based on a smooth running of the effective Planck mass. The model introduces a single additional parameter, ε₀, which modifies the effective gravitational coupling only at late cosmic times, while leaving early-universe physics unchanged. The primary motivation is the persistent S₈ tension between CMB-inferred and late-time structure-growth measurements. We demonstrate that for ε₀ ≈ 0.015–0.02, the model produces a controlled 2–3% suppression of structure growth. Crucially, this suppression: • leaves primary CMB anisotropies unchanged• preserves Big Bang nucleosynthesis• maintains c_T = 1• satisfies Solar System bounds on Ḡ/G• introduces no ghosts or higher-derivative instabilities The framework remains fully consistent within effective field theory and is straightforwardly implementable in Boltzmann solvers such as CLASS. Importantly, the model is distinguishable from wCDM, as it modifies the gravitational coupling directly rather than altering only the background expansion. The predicted observational signatures can be tested through combined analyses of RSD, weak lensing, and CMB–LSS cross-correlations. The work does not aim to replace ΛCDM but to explore a minimal and controlled late-time deformation of gravity that may address a specific observational discrepancy. We believe the manuscript will be of interest to the cosmology and modified gravity communities.