Quantum Informational Gravity (QIG): A Unified φR + φF² Lagrangian Linking Curvature, Quantum Fields, and the Dark Sector

Quantum-Informational Gravity (QIG) provides a unified scalar-field framework that connects dark matter, dark energy, and information geometry through a single, canonical Lagrangian. This release contains the complete Overleaf/arXiv source files and the updated analytic formulation of both the scalar-field dark-matter model and the QIG information manifold.

The technical content includes:

the full scalar-field action and Euler–Lagrange equations,

background evolution across slow-roll, kinetic, and oscillatory regimes,

derivation of the effective equation of state and CDM-like behavior,

linear perturbation equations in Newtonian gauge,

analytic expressions for the microscopic and effective sound speeds,

Jeans scale evolution and clustering criteria,

viability constraints from Lyman-α, structure formation, and oscillation onset,

stability conditions ensuring the absence of ghost, tachyonic, or gradient instabilities.

The QIG extension introduces a convex information manifold that constrains probabilistic state evolution and provides a geometric alternative to conventional linear embedding spaces. This structure mitigates instability modes and precision-loss accumulation and offers a principled explanation for hallucination behavior in multi-head attention architectures.

Scope and Assumptions:

The analysis is performed strictly within general relativity, a canonical kinetic term, and smooth potentials. No new forces, exotic interactions, or nonstandard gravitational terms are introduced. The results serve as a concise, unified reference for canonical scalar-field phenomenology.

Limitations and Future Work:

Nonlinear structure formation, full Boltzmann-code analysis (CLASS/CAMB), and UV model-building lie outside the present scope and are reserved for follow-up work.

This archive provides a reproducible and canonical baseline for scalar-field dark-matter studies and the continued development of the QIG formalism.