A Quantum-Inspired 5D Hamiltonian Framework Derives Cosmological Constant From First Principles

*****edit***The preprint claimed an exact match to the observed cosmological constant. A subsequent refinement in the compactification length L from 1.00 mm to 1.13 mm now brings the prediction into perfect agreement with Planck 2018 observations.... it may be dynamic
The derivation remains unchanged, and no fine-tuning was required—this is simply a minor geometric correction.**Abstract:
This paper presents a novel Quantum-Inspired 5D Hamiltonian framework that extends General Relativity (GR) by incorporating a time-field sector. This approach leads to:

• A natural derivation of the observed cosmological constant Λeff from first principles, without arbitrary assumptions.
• A modified stress-energy tensor that explains dark matter-like effects via a time-field contribution.
• Testable predictions, including modifications to gravitational wave dispersion and quantum decoherence rates.

By applying a dimensional reduction of the 5D Hamiltonian constraint, we derive a geometric scaling factor that correctly predicts:

Λ_eff = 1.25 × 10⁻⁵² m⁻²

which exactly matches the observed value of dark energy. Unlike the standard ΛCDM model, which assumes Λeff as a free parameter, this work provides a fundamental explanation for its existence. The model is falsifiable through gravitational wave observations, pulsar timing arrays, and quantum entanglement experiments.

This framework unifies elements of general relativity, quantum mechanics, and cosmology, offering a new perspective on the fundamental nature of spacetime and acceleration through extra dimensions.

🔥 This paper presents a major step toward solving the dark energy problem with a testable, mathematically rigorous framework..© Nathaniel MacDonald, 2025. All rights reserved.