Theoretical Foundations of the Holographic Axion: Geometric Derivations, Thermodynamics, and Numerical Engine.
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2026
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| _version_ | 1866901720292917248 |
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| author | Emilano G., Greco |
| author_facet | Emilano G., Greco |
| contents | <div> <p>This document serves as the mathematical foundation for the paper “The Holographic Axion: Inertial Freezing and the Geometric Origin of Dark Energy”. We provide the explicit derivations and numerical architecture validating the geometric unification of the dark sector.</p> <p><strong>1. The Geometric Seesaw:</strong> We derive the Dark Energy scale (ΛDE ≈ 2.4 meV) from first principles via the warped Aharonov–Bohm effect. We demonstrate that this scale is not fine‑tuned, but is generated by the “Geometric Seesaw” relation ΛDE ≈ ΛIR² / MP l, rigidly fixed by the F‑Theory confinement scale ΛIR ≈ 55.3 TeV (flux K = 3).</p> <p><strong>2. The Dark Trigger (zc ≈ 4225):</strong> We model the onset of cosmic acceleration as a thermodynamic Hawking–Page phase transition in the bulk. Using the critical exponent n = 3, compatible with a fast holographic detonation (β/H ≈ 100), we predict activation of the axion potential at a critical redshift zc ≈ 4225, injecting Early Dark Energy and alleviating the Hubble tension (H0 ≈ 72.1 km/s/Mpc).</p> <p><strong>3. Inertial Freezing and S8 Resolution:</strong> Our numerical engine (LSODA) reveals a three‑phase dynamics: a high‑redshift stiff regime (w = 1) consistent with BBN, a vacuum‑capture stage, and a late‑time thawing phase (w0 ≈ −0.967). We explicitly derive the dark‑sector coupling β ≈ 0.05 required to resolve the S8 tension, showing that it arises naturally from the “Volume Dilution” of wavefunctions in the bulk volume V = 10π fixed by fluxes.</p> <p><strong>4. Stability Certification:</strong> We demonstrate that the model is ghost‑free, satisfies the Null Energy Condition, and is fully compatible with the Yang–Mills mass gap via the principle of adiabatic continuity and sector separation.</p> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18709390 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Theoretical Foundations of the Holographic Axion: Geometric Derivations, Thermodynamics, and Numerical Engine. Emilano G., Greco Kaluza-Klein Reduction 5D Effective Field Theory Geometric Phase Transitions Instanton Physics Numerical Relativity Python Code Holographic Dark Energy Geometric Seesaw F-Theory Fluxes Hawking-Page Transition Inertial Freezing S8 Tension <div> <p>This document serves as the mathematical foundation for the paper “The Holographic Axion: Inertial Freezing and the Geometric Origin of Dark Energy”. We provide the explicit derivations and numerical architecture validating the geometric unification of the dark sector.</p> <p><strong>1. The Geometric Seesaw:</strong> We derive the Dark Energy scale (ΛDE ≈ 2.4 meV) from first principles via the warped Aharonov–Bohm effect. We demonstrate that this scale is not fine‑tuned, but is generated by the “Geometric Seesaw” relation ΛDE ≈ ΛIR² / MP l, rigidly fixed by the F‑Theory confinement scale ΛIR ≈ 55.3 TeV (flux K = 3).</p> <p><strong>2. The Dark Trigger (zc ≈ 4225):</strong> We model the onset of cosmic acceleration as a thermodynamic Hawking–Page phase transition in the bulk. Using the critical exponent n = 3, compatible with a fast holographic detonation (β/H ≈ 100), we predict activation of the axion potential at a critical redshift zc ≈ 4225, injecting Early Dark Energy and alleviating the Hubble tension (H0 ≈ 72.1 km/s/Mpc).</p> <p><strong>3. Inertial Freezing and S8 Resolution:</strong> Our numerical engine (LSODA) reveals a three‑phase dynamics: a high‑redshift stiff regime (w = 1) consistent with BBN, a vacuum‑capture stage, and a late‑time thawing phase (w0 ≈ −0.967). We explicitly derive the dark‑sector coupling β ≈ 0.05 required to resolve the S8 tension, showing that it arises naturally from the “Volume Dilution” of wavefunctions in the bulk volume V = 10π fixed by fluxes.</p> <p><strong>4. Stability Certification:</strong> We demonstrate that the model is ghost‑free, satisfies the Null Energy Condition, and is fully compatible with the Yang–Mills mass gap via the principle of adiabatic continuity and sector separation.</p> </div> |
| title | Theoretical Foundations of the Holographic Axion: Geometric Derivations, Thermodynamics, and Numerical Engine. |
| topic | Kaluza-Klein Reduction 5D Effective Field Theory Geometric Phase Transitions Instanton Physics Numerical Relativity Python Code Holographic Dark Energy Geometric Seesaw F-Theory Fluxes Hawking-Page Transition Inertial Freezing S8 Tension |
| url | https://doi.org/10.5281/zenodo.18709390 |