Residual Λeff in a Gauged Constant Vacuum-Mode (GCV) Framework: A "Squashing-Remnant" Interpretation
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2025
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| _version_ | 1866902085357797376 |
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| author | Johansson, Germund |
| author_facet | Johansson, Germund |
| contents | <p>This note is part of the gauged constant vacuum‑mode (GCV) programme. In GCV, strictly spacetime‑constant matter‑sector vacuum energy is treated as a gauge degree of freedom and removed from the local Einstein equations by a three‑/four‑form sector, while local excitations gravitate normally. On the minimal GR‑exact branch the field equations reduce to GR with a flux‑fixed effective cosmological constant Λ_eff, so late‑time cosmology is indistinguishable from flat ΛCDM once Λ_eff is fixed by data.</p> <p>The note gives an interpretation of the observed small positive Λ_eff as a residual “squashing remnant” of the global neutralisation of large vacuum contributions by the light mediator, rather than as an independent sector or hand‑tuned constant. It also records a simple two‑flux discretuum toy and an EFT‑level “mediator existence” example that realise a small Λ_eff and a small non‑zero mediator amplitude within the same framework, consistent with the broader GCV / CCP_DE / CCP_DE_step3 / RulerFree programme.</p> <p><strong>Changes in v2.1.1 (2025-11-30):</strong><br>- Added an explicit remark in the main text that, even in the simple two-flux toy, there are multiple flux configurations whose Λ_eff values lie very close to zero, and that realistic multi-flux discretua will contain an enormous number of such near-zero levels.<br>- Clarified that a given Hubble patch simply occupies one of these near-zero flux vacua, so the small residual Λ_eff should be viewed as the flux label of whichever “crack in the armour” that patch lives in, rather than as a continuously tunable parameter.<br>- Minor wording tweaks to keep the squashing-remnant interpretation and the flux-discretuum picture aligned with the GR-exact GCV construction and its companion notes (CCP_GRexact, CCP_DE, CCP_DE_step3, EarlyUniverse, RulerFree, Practical Cosmology).</p> <p><strong>Changes in v2.1.0 (2025‑11‑30)</strong></p> <ul> <li> <p>Refines the two‑flux discretuum toy used to illustrate the squashing‑remnant picture. The scan over (n₁, n₂) and Λ₀ is now explicitly described, with Λ_eff = 0 at (±20, 0) and the smallest positive level Λ_eff ≃ 6.125×10⁻⁴ at (±14, ±11).</p> </li> <li> <p>Clarifies that the two‑flux model is a dimensionless cartoon and that realistic multi‑flux discretua (as in CCP_GRexact) are required to reach Λ_eff at the observed dark‑energy scale.</p> </li> <li> <p>Makes explicit that the question of whether metastability plus structure‑formation cuts statistically favour small positive Λ_eff is left as an open problem for future work.</p> </li> <li> <p>Minor editorial updates (version labels, DOIs, and author footnote with homepage johansson.digital).</p> </li> </ul> <p><strong>Version history</strong></p> <p><strong>v2.0.0</strong><br>This update turned the earlier, purely conceptual residual‑Λ note into a more concrete existence proof within the GCV framework. The strictly spacetime‑constant vacuum mode is treated as a gauge‑controlled, flux‑fixed degree of freedom, so the local Einstein equations are exactly GR plus a residual Λ_eff, while all local excitations gravitate normally.</p> <p>v2.0.0 kept the basic “squashing‑remnant” interpretation of Λ_eff – as the tiny leftover of the global neutralisation of large vacuum contributions by a light three/four‑form mediator – but made it explicit in three ways:</p> <ol> <li> <p>A simple two‑flux discretuum toy where modest integer fluxes already produce very small positive Λ_eff, illustrating how a realistic remnant can arise without extreme numbers.</p> </li> <li> <p>A demonstration that such a remnant can coexist with a small, symmetry‑protected mediator amplitude ε that induces only percent‑level deviations in late‑time growth, matching the linear‑response µ(a) = ε f(a) phenomenology developed in CCP_DE_step3.</p> </li> <li> <p>An explanation of how this maps onto the late‑time AP+RSD compression in the RulerFree data note, where the AP track sees the Λ‑like geometry while the tiny RSD block would be sensitive to the same mediator.</p> </li> </ol> <p>The scope remained conservative: v2.0.0 did not claim a unique selection mechanism for Λ_eff, did not alter any quantitative fits in the companion GCV / CCP_DE / RulerFree materials, and did not add new data analysis. Its role was to (i) sharpen the interpretation of Λ_eff as a “flux‑fixed squashing remnant”, (ii) exhibit an explicit toy discretuum where tiny positive values are easy to obtain, and (iii) tie that picture to the one‑parameter linear‑response and ruler‑free late‑time phenomenology used elsewhere in the programme.</p> <p><strong>v1.1.0</strong><br>A largely conceptual version that recorded the squashing‑remnant interpretation, illustrated it with a simple two‑flux discretuum toy, and explicitly left fully quantitative flux models and detailed phenomenological tests to future work.</p> <p><strong>v1.0.0</strong><br>The original short note introducing the residual, flux‑fixed cosmological constant Λ_eff in the GCV framework. It emphasised Λ_eff as a global, topological residual rather than a conventional local coupling, surveyed simple “selection” routes for a tiny positive value (flux discretuum, membrane transitions, statistical/anthropic filters), and explained how these could be implemented without spoiling radiative stability or GR‑exactness of the low‑energy sector. It also sketched how this picture dovetails with the late‑time dark‑energy phenomenology and null tests (CCP_DE, CCP_DE_step3), the early‑Universe extension with inflation and phase transitions (GCV_EarlyUniverse), and the practical ruler‑free AP+RSD compression for late‑time data (RulerFree, GCV_PracticalCosmology).</p> <p>Programme overview, companion notes and updates:<br>https://johansson.digital</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17768325 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Residual Λeff in a Gauged Constant Vacuum-Mode (GCV) Framework: A "Squashing-Remnant" Interpretation Johansson, Germund cosmological constant problem vacuum energy sequestering gauged constant vacuum (GCV) three‑form / four‑form flux residual Λ_eff dark energy modified gravity (EFT of DE) early‑universe cosmology large‑scale structure Astrophysics – Cosmology and Nongalactic Astrophysics (astro‑ph.CO) General Relativity and Quantum Cosmology (gr‑qc) Dark energy and modified gravity Theoretical cosmology <p>This note is part of the gauged constant vacuum‑mode (GCV) programme. In GCV, strictly spacetime‑constant matter‑sector vacuum energy is treated as a gauge degree of freedom and removed from the local Einstein equations by a three‑/four‑form sector, while local excitations gravitate normally. On the minimal GR‑exact branch the field equations reduce to GR with a flux‑fixed effective cosmological constant Λ_eff, so late‑time cosmology is indistinguishable from flat ΛCDM once Λ_eff is fixed by data.</p> <p>The note gives an interpretation of the observed small positive Λ_eff as a residual “squashing remnant” of the global neutralisation of large vacuum contributions by the light mediator, rather than as an independent sector or hand‑tuned constant. It also records a simple two‑flux discretuum toy and an EFT‑level “mediator existence” example that realise a small Λ_eff and a small non‑zero mediator amplitude within the same framework, consistent with the broader GCV / CCP_DE / CCP_DE_step3 / RulerFree programme.</p> <p><strong>Changes in v2.1.1 (2025-11-30):</strong><br>- Added an explicit remark in the main text that, even in the simple two-flux toy, there are multiple flux configurations whose Λ_eff values lie very close to zero, and that realistic multi-flux discretua will contain an enormous number of such near-zero levels.<br>- Clarified that a given Hubble patch simply occupies one of these near-zero flux vacua, so the small residual Λ_eff should be viewed as the flux label of whichever “crack in the armour” that patch lives in, rather than as a continuously tunable parameter.<br>- Minor wording tweaks to keep the squashing-remnant interpretation and the flux-discretuum picture aligned with the GR-exact GCV construction and its companion notes (CCP_GRexact, CCP_DE, CCP_DE_step3, EarlyUniverse, RulerFree, Practical Cosmology).</p> <p><strong>Changes in v2.1.0 (2025‑11‑30)</strong></p> <ul> <li> <p>Refines the two‑flux discretuum toy used to illustrate the squashing‑remnant picture. The scan over (n₁, n₂) and Λ₀ is now explicitly described, with Λ_eff = 0 at (±20, 0) and the smallest positive level Λ_eff ≃ 6.125×10⁻⁴ at (±14, ±11).</p> </li> <li> <p>Clarifies that the two‑flux model is a dimensionless cartoon and that realistic multi‑flux discretua (as in CCP_GRexact) are required to reach Λ_eff at the observed dark‑energy scale.</p> </li> <li> <p>Makes explicit that the question of whether metastability plus structure‑formation cuts statistically favour small positive Λ_eff is left as an open problem for future work.</p> </li> <li> <p>Minor editorial updates (version labels, DOIs, and author footnote with homepage johansson.digital).</p> </li> </ul> <p><strong>Version history</strong></p> <p><strong>v2.0.0</strong><br>This update turned the earlier, purely conceptual residual‑Λ note into a more concrete existence proof within the GCV framework. The strictly spacetime‑constant vacuum mode is treated as a gauge‑controlled, flux‑fixed degree of freedom, so the local Einstein equations are exactly GR plus a residual Λ_eff, while all local excitations gravitate normally.</p> <p>v2.0.0 kept the basic “squashing‑remnant” interpretation of Λ_eff – as the tiny leftover of the global neutralisation of large vacuum contributions by a light three/four‑form mediator – but made it explicit in three ways:</p> <ol> <li> <p>A simple two‑flux discretuum toy where modest integer fluxes already produce very small positive Λ_eff, illustrating how a realistic remnant can arise without extreme numbers.</p> </li> <li> <p>A demonstration that such a remnant can coexist with a small, symmetry‑protected mediator amplitude ε that induces only percent‑level deviations in late‑time growth, matching the linear‑response µ(a) = ε f(a) phenomenology developed in CCP_DE_step3.</p> </li> <li> <p>An explanation of how this maps onto the late‑time AP+RSD compression in the RulerFree data note, where the AP track sees the Λ‑like geometry while the tiny RSD block would be sensitive to the same mediator.</p> </li> </ol> <p>The scope remained conservative: v2.0.0 did not claim a unique selection mechanism for Λ_eff, did not alter any quantitative fits in the companion GCV / CCP_DE / RulerFree materials, and did not add new data analysis. Its role was to (i) sharpen the interpretation of Λ_eff as a “flux‑fixed squashing remnant”, (ii) exhibit an explicit toy discretuum where tiny positive values are easy to obtain, and (iii) tie that picture to the one‑parameter linear‑response and ruler‑free late‑time phenomenology used elsewhere in the programme.</p> <p><strong>v1.1.0</strong><br>A largely conceptual version that recorded the squashing‑remnant interpretation, illustrated it with a simple two‑flux discretuum toy, and explicitly left fully quantitative flux models and detailed phenomenological tests to future work.</p> <p><strong>v1.0.0</strong><br>The original short note introducing the residual, flux‑fixed cosmological constant Λ_eff in the GCV framework. It emphasised Λ_eff as a global, topological residual rather than a conventional local coupling, surveyed simple “selection” routes for a tiny positive value (flux discretuum, membrane transitions, statistical/anthropic filters), and explained how these could be implemented without spoiling radiative stability or GR‑exactness of the low‑energy sector. It also sketched how this picture dovetails with the late‑time dark‑energy phenomenology and null tests (CCP_DE, CCP_DE_step3), the early‑Universe extension with inflation and phase transitions (GCV_EarlyUniverse), and the practical ruler‑free AP+RSD compression for late‑time data (RulerFree, GCV_PracticalCosmology).</p> <p>Programme overview, companion notes and updates:<br>https://johansson.digital</p> |
| title | Residual Λeff in a Gauged Constant Vacuum-Mode (GCV) Framework: A "Squashing-Remnant" Interpretation |
| topic | cosmological constant problem vacuum energy sequestering gauged constant vacuum (GCV) three‑form / four‑form flux residual Λ_eff dark energy modified gravity (EFT of DE) early‑universe cosmology large‑scale structure Astrophysics – Cosmology and Nongalactic Astrophysics (astro‑ph.CO) General Relativity and Quantum Cosmology (gr‑qc) Dark energy and modified gravity Theoretical cosmology |
| url | https://doi.org/10.5281/zenodo.17768325 |