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

Description:

This work introduces a single new Lagrangian term that unifies gravity, quantum fields, dark matter and dark energy into one mechanism.

 By adding an “informational field” φ with two couplings—φR to curvature and φF² to quantum fluctuations—the model creates a direct bridge between spacetime geometry and the quantum vacuum.

The result is a testable scalar–tensor framework that reproduces cosmic acceleration, mimics dark-matter clustering, and links vacuum energy to curvature without new particles or exotic physics.

 A single field, one equation, and an experimentally constrained pathway to unifying GR and quantum mechanics.

The proposed “informational Lagrangian” is

> L_φ = ½ (∂φ)·(∂φ) − V(φ) + α φ R + β φ F_{\muν} F^{\muν},

where R is the Ricci scalar (curvature), F_{\muν} is the electromagnetic field tensor, and α and β are coupling constants. This term couples information (φ), geometry (R) and quantum/EM fluctuations (F²) in one unified structure.

The result is a scalar–tensor informational field theory (IFT) that can be written in standard Einstein frame and tested directly against cosmological data (Planck, DESI, SN1a, CMB and LSS).

Key Contributions

1. New informational field and Lagrangian

The φ-field is introduced as a physical carrier of information with its own kinetic term, potential V(φ), and two key couplings:

α φ R : non-minimal coupling to curvature (modified gravity),

β φ F² : coupling to electromagnetic/quantum fluctuations (the “Quantum Bridge”).

2. Single mechanism for dark matter and dark energy

In the Einstein-frame cosmology, the φ-field reproduces both dark sectors without adding new particle species.

A plateau-type potential U(χ) for the canonically normalized field χ drives late-time acceleration and yields a dark-energy equation of state w(a) that can match current DESI + SN1a constraints.

A scale-dependent effective Newton constant G_eff(k) arising from the φ–curvature coupling mimics dark-matter–like clustering on galactic and cosmological scales.

3. Quantum Bridge between vacuum fluctuations and curvature

The β φ F² term links quantum vacuum fluctuations directly to the φ-field, which in turn feeds back into curvature. This defines a “Quantum Bridge” from quantum fields to gravity and offers a concrete mechanism for connecting vacuum energy, dark energy and spacetime geometry inside a single action.

4. Information as a conserved physical quantity

Because φ carries energy density and pressure and appears in the total stress–energy tensor, information behaves as a conserved physical quantity (like energy–momentum) rather than an abstract bookkeeping device. This has implications for black-hole information, horizon thermodynamics and any system where information flow and curvature interact.

5. Complete, testable cosmology framework

The manuscript collects the full 15-equation set needed for realistic tests:

Einstein-frame action with the informational field,

scalar energy density and pressure,

modified Friedmann equations with ρ_φ,

scalar equation of motion on an FRW background,

full Einstein equations with φ-coupling,

stress–energy tensor of the informational field,

modified Maxwell equation from the β-term,

Klein–Gordon equation in curved space,

conformal transformation (Jordan ↔ Einstein frame),

canonical field redefinition χ(φ),

linear perturbation equation with G_eff,

sound-speed condition c_s² = 1,

inflationary tensor-to-scalar prediction r(λ, N),

dark-energy equation of state w(a),

and observational consistency conditions (Planck, DESI, SN1a).

Taken together, these results define a fully specified, scalar–tensor informational field theory:

 in which gravity, quantum fluctuations, dark energy, dark-matter–like effects, mass generation and information flow all emerge from the dynamics of a single φ-field.

This Zenodo release is intended as an open, citable reference for researchers evaluating the Informational Field Theory / QIG framework and its observational consequences.