A Maximum-Entropy Single-Scale Modification of Gravity and its Cosmological Signature

### OverviewThis record contains the preprint/paper introducing a novel, single-parameter theoretical framework for scale-dependent infrared (IR) modifications of gravity. Designed as a principled, methodological benchmark rather than a microscopic derivation, the model addresses the persistent S₈ tension between early-universe CMB data and late-time weak lensing surveys. ### Core MethodologyInstead of introducing multiple free parameters or arbitrary functions, we combine three strict structural requirements with Jaynes' Maximum-Entropy principle: 1. **Positive Spectral Representation: ** Adherence to a Källén–Lehmann form ensuring a ghost-free structure. 2. **UV Recovery: ** Smooth and exact interpolation back to standard General Relativity at small scales. 3. **Single Coherence Scale (L): ** Maximizing the Shannon entropy under a single first-moment constraint m² = L^-2 uniquely singles out an exponential spectral density. This yields a non-local gravitational coupling kernel governed by the exponential integral: J (k² L²) = k² L² \, e^k² L² \, E₁ (k² L²) ### Cosmological Relevance & Predictions* **S₈ Tension Resolution: ** A heuristic fit to the KiDS-1000 central value yields a characteristic scale of L 121\, h^-1\, Mpc (170\, Mpc for h = 0. 7). * **Sharp Falsifiability: ** Unlike multi-parameter modified gravity models (e. g. , f (R) or Horndeski theories), the functional shape of the lensing consistency deviation (k) is fixed entirely by the architecture of the kernel. Only the horizontal scale transition (L) remains free, making the model highly vulnerable to immediate falsification by upcoming data releases from Euclid, LSST, and DESI. ### Contents of this Record* G-mod. pdf` / `manuscript. tex`: The full scientific text including analytical derivations of the kernel's asymptotics, the modified Poisson equation, and comparisons with existing modified gravity frameworks. ### KeywordsModified Gravity, Cosmology, S8 Tension, Maximum Entropy Principle, Källén-Lehmann Representation, Weak Lensing, Non-local Gravity.