Information-Driven Gravity (IDG) as a Constrained Scalar-Tensor Extension of ΛCDM (v4 Quantitative Results Added)

**Information-Driven Gravity as a Constrained Scalar-Tensor Extension of ΛCDM ** This work presents an implementation and empirical evaluation of an Information-Driven Gravity (IDG) framework formulated as a scalar-tensor extension to the standard ΛCDM cosmological model. The model introduces a subdominant scalar field component, parameterized by a present-day density fraction Ωₛcf and coupling parameter λ, designed to preserve consistency with established cosmological observables while allowing for controlled deviations from General Relativity. The IDG model is implemented within the CLASS Boltzmann solver and constrained using MontePython through Markov Chain Monte Carlo (MCMC) sampling. Observational datasets include Planck CMB likelihoods and the Pantheon Type Ia supernova compilation, ensuring compatibility with current high-precision cosmological measurements. Results demonstrate that the model remains consistent with ΛCDM within observational uncertainties, with Ωₛcf constrained to small values (≲ 10⁻³–10⁻²) and no statistically significant improvement in χ² relative to the ΛCDM baseline. Gravitational slip remains effectively unity across relevant scales and redshifts, indicating observational degeneracy at current sensitivity levels. A key outcome of this analysis is the identification of a tension between observational constraints and detectability thresholds: parameter regimes capable of producing measurable deviations in gravitational slip are currently disfavored by Planck data. This positions IDG within the class of constrained or hidden-sector modifications of gravity, consistent with existing observations yet structured for potential detection by next-generation surveys such as Euclid. Version 4 of this release introduces a quantitative results summary table derived from MCMC parameter inference, clarifying parameter constraints and strengthening the empirical grounding of the analysis. The theoretical framework and numerical implementation remain unchanged from Version 1. --- Key Features - Implementation of a scalar-tensor modification within CLASS- Full MCMC parameter inference using MontePython- Constraints from Planck CMB and Pantheon supernova data- Identification of detectability–constraint tension- Preservation of ΛCDM limit (Ωₛcf → 0) --- ReproducibilityThis work is fully reproducible using publicly available tools: - CLASS (Cosmic Linear Anisotropy Solving System) - MontePython (cosmological parameter inference) - Planck likelihoods- Pantheon dataset --- Version NotesVersion 4: - Added quantitative results table- Clarified parameter constraints and χ² comparison- Improved presentation of empirical findings- No changes to theoretical model or simulation pipeline