Systematic next-to-leading-order expansion of the conformal scalar response equation and numerical control benchmarks
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| Format: | Recurso digital |
| Sprache: | Englisch |
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2026
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| _version_ | 1866901072286580736 |
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| author | Flügge, Jan-Frederik |
| author_facet | Flügge, Jan-Frederik |
| contents | <p>We present a systematic next-to-leading-order (NLO) expansion of the conformal scalar field equation within the Vacuum Field Theory (VFT) framework. Motivated by empirical tensions in the leading-order (LO) monopolar model, we derive the exact non-linear perturbation equation from the covariant action and isolate the quadratic NLO source functional. We demonstrate analytically that this functional cleanly separates into a renormalisable monopolar sector and an irreducible non-monopolar (<span><span><span><span><span>ℓ</span><span>≥</span></span><span><span>2</span></span></span></span></span>) channel. This non-monopolar remainder provides the rigorous theoretical origin for the previously identified morphology-dependent response (<span><span><span><span><span>Q</span></span></span></span></span>-channel), replacing ad-hoc operational proxies.</p> <p>We conduct numerical control benchmarks in the canonical-kinetic limit across a range of baryonic source geometries. The benchmarks establish that the NLO correction is perturbatively controlled and exhibits a strict morphology-coupling factorisation:</p> <ol> <li> <p><strong>Spherical Control:</strong> For perfectly spherical sources, the non-monopolar NLO correction vanishes identically.</p> </li> <li> <p><strong>Aspherical Activation:</strong> For axisymmetric toy models and regularised bulge+disk geometries, the irreducible quadrupolar fraction is monotonically activated by baryonic disk flattening and disk dominance.</p> </li> <li> <p><strong>Coupling Modulation:</strong> The absolute amplitude of the activated channel is scaled by the coupling-gradient coefficient (<span><span><span><span><span><span>α</span><span><span><span><span><span><span><span>1</span></span></span></span><span></span></span></span></span></span></span></span></span></span>).</p> </li> <li> <p><strong>Solar-System Viability:</strong> A local benchmark confirms that the small solar oblateness (<span><span><span><span><span><span>J</span><span><span><span><span><span><span><span>2</span></span></span></span><span></span></span></span></span></span></span></span></span></span>) generates a negligible NLO acceleration (<span><span><span><span><span>∼</span></span><span><span>1</span><span>0<span><span><span><span><span><span><span>−6</span></span></span></span></span></span></span></span><span><span>g</span><span><span><span><span><span><span><span>N</span></span></span></span><span></span></span></span></span></span></span></span></span></span> at 1 AU), avoiding immediate conflict with precision-gravity constraints like Cassini.</p> </li> </ol> <p>These results establish the existence, local viability, and astrophysical robustness of the morphology-activated NLO scalar response. They provide a fully covariant, structured foundation for upcoming quantitative confrontations with galactic rotation curves.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19036574 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Systematic next-to-leading-order expansion of the conformal scalar response equation and numerical control benchmarks Flügge, Jan-Frederik Galaxy dynamics galaxy kinematics modified gravity Dark matter scalar tensor <p>We present a systematic next-to-leading-order (NLO) expansion of the conformal scalar field equation within the Vacuum Field Theory (VFT) framework. Motivated by empirical tensions in the leading-order (LO) monopolar model, we derive the exact non-linear perturbation equation from the covariant action and isolate the quadratic NLO source functional. We demonstrate analytically that this functional cleanly separates into a renormalisable monopolar sector and an irreducible non-monopolar (<span><span><span><span><span>ℓ</span><span>≥</span></span><span><span>2</span></span></span></span></span>) channel. This non-monopolar remainder provides the rigorous theoretical origin for the previously identified morphology-dependent response (<span><span><span><span><span>Q</span></span></span></span></span>-channel), replacing ad-hoc operational proxies.</p> <p>We conduct numerical control benchmarks in the canonical-kinetic limit across a range of baryonic source geometries. The benchmarks establish that the NLO correction is perturbatively controlled and exhibits a strict morphology-coupling factorisation:</p> <ol> <li> <p><strong>Spherical Control:</strong> For perfectly spherical sources, the non-monopolar NLO correction vanishes identically.</p> </li> <li> <p><strong>Aspherical Activation:</strong> For axisymmetric toy models and regularised bulge+disk geometries, the irreducible quadrupolar fraction is monotonically activated by baryonic disk flattening and disk dominance.</p> </li> <li> <p><strong>Coupling Modulation:</strong> The absolute amplitude of the activated channel is scaled by the coupling-gradient coefficient (<span><span><span><span><span><span>α</span><span><span><span><span><span><span><span>1</span></span></span></span><span></span></span></span></span></span></span></span></span></span>).</p> </li> <li> <p><strong>Solar-System Viability:</strong> A local benchmark confirms that the small solar oblateness (<span><span><span><span><span><span>J</span><span><span><span><span><span><span><span>2</span></span></span></span><span></span></span></span></span></span></span></span></span></span>) generates a negligible NLO acceleration (<span><span><span><span><span>∼</span></span><span><span>1</span><span>0<span><span><span><span><span><span><span>−6</span></span></span></span></span></span></span></span><span><span>g</span><span><span><span><span><span><span><span>N</span></span></span></span><span></span></span></span></span></span></span></span></span></span> at 1 AU), avoiding immediate conflict with precision-gravity constraints like Cassini.</p> </li> </ol> <p>These results establish the existence, local viability, and astrophysical robustness of the morphology-activated NLO scalar response. They provide a fully covariant, structured foundation for upcoming quantitative confrontations with galactic rotation curves.</p> |
| title | Systematic next-to-leading-order expansion of the conformal scalar response equation and numerical control benchmarks |
| topic | Galaxy dynamics galaxy kinematics modified gravity Dark matter scalar tensor |
| url | https://doi.org/10.5281/zenodo.19036574 |