Entropic ScalarInflation:AUnified Framework for Cosmological Expansion and Near Scale-Invariant Inflation

We present a comprehensive analysis of the Entropic Scalar Inflation (ESI) model, a unified framework that combines scalar field dynamics with entropy-driven corrections to describe both early-universe inflation and late-time cosmic acceleration. The model modifies standard Friedmann dynamics by incorporating an information-theoretic entropy term S = (1 + a) or S = (1 + a), where is the entropy strength parameter. We derive the entropy term from first principles using holographic entanglement entropy, showing that = H₀²/ (2²) is an emergent thermodynamic coefficient determined by the logarithmic correction coefficient, not a free phenomenological parameter. We conduct extensive observational tests using DESI (Dark Energy Spectroscopic Instrument) data, Pantheon+ supernova measurements, and cosmic chronometers H (z) data. The model demonstrates strong performance across five core test categories: initial background expansion yields ² -9 relative to CDM; refined logarithmic background expansion gives ² = -9. 2; parameter estimation yields ₘ = 0. 23 0. 01, = -0. 05 0. 01, H₀ = 70. 1 1. 2; and residual analysis shows improved consistency. The AIC/BIC analysis confirms that the ESI model is statistically preferred over CDM despite having one additional parameter. Inflationary predictions produce a spectral index nₛ = 0. 9667 and tensor-to-scalar ratio r = 0. 0031, consistent with near scale-invariant perturbations. The model naturally explains dark energy as an emergent entropy-driven phenomenon while preserving the successful predictions of inflationary cosmology. Preliminary CMB constraints from the angular diameter distance are consistent with Planck data. Future work will extend the analysis to full CMB power spectrum constraints using modified CAMB implementations.