CMB Compatibility and the Dissolution of the Mass Hierarchy in the Elastic Vacuum

This paper addresses three open questions carried from Papers 5 and 6 of the elastic vacuum programme: the 10⁵⁵ mass hierarchy between the inflationary scalaron and the late-time screening field, quantitative compatibility with the cosmic microwave background (CMB), and numerical confirmation of the flatness feedback parameter β > 0 beyond the quasi-static approximation.

Two principal results are delivered. First, the mass hierarchy is dissolved within standard effective field theory. The full gravitational effective action supports different effective degrees of freedom at different background curvatures: at inflationary curvature R ~ M², the R² correction yields a heavy scalaron (derived via conformal transformation), while at late-time curvature R ~ H₀², the screening field ψ with mass m_ψ ~ H₀ operates from a different sector of the same action (postulated on phenomenological grounds and shown to be consistent with the EFT framework). These are distinct excitation branches of the same elastic medium, analogous to optical phonons and seismic waves in a crystalline solid. The dissolution is explicitly asymmetric: the high-curvature mode is derived, the low-curvature mode is assumed. No single field is required to span 55 orders of magnitude.

Second, CMB compatibility is established. At recombination (z ≈ 1089), the screening field is frozen in its saturated quasi-static configuration, contributing less than one part in 10⁹ to the total energy density. The ψ-perturbations are suppressed by a factor ~10⁻¹¹ relative to matter perturbations on CMB scales—far below Planck sensitivity. The acoustic peak structure (positions, heights, damping tail) is preserved. Heuristic scaling estimates suggest an enhanced integrated Sachs–Wolfe (ISW) effect from differential screening in cosmic voids as a qualitative indication of where the framework first departs from ΛCDM; quantitative confirmation requires Boltzmann code implementation.

Additionally, a full dynamical solution of the coupled (ψ, a, K) system—using the complete Starobinsky potential and deriving Ω_K from the Friedmann equation without pre-assuming the β-dependent form—confirms β_eff > 0 at all tested epochs and for multiple parameter choices (ξ = 0.01, 0.05, 0.1), completing the flatness attractor proof deferred from Papers 5 and 6.

The paper identifies a lower bound on the coupling parameter ξ from internal consistency requirements and proposes a conjunction test (w ≠ −1 with w₀ > −1, scale-dependent growth at k ~ H₀, and μ = Σ = 1) as the framework's distinctive observational signature. The most significant limitation is the absence of a full Boltzmann code (CLASS/CAMB) analysis, identified as the highest priority for future work.

Recommended for submission to the Journal of Cosmology and Astroparticle Physics (JCAP).

Programme context: This paper follows Paper 5 ("The Elastic Vacuum," Kriger 2025) and Paper 6 ("Connection of Vacuum Energy with Inflation," Kriger 2026a). It precedes Paper 8 (structure growth) and Paper 9 (N-body simulations) in the programme sequence.

Keywords: elastic vacuum; CMB compatibility; mass hierarchy; effective field theory; vacuum energy screening; flatness problem; cosmological perturbations; integrated Sachs–Wolfe effect; Starobinsky inflation; cosmological constant problem; dark energy; modified gravity

License: Creative Commons Attribution 4.0 International (CC BY 4.0)

Language: English

Related identifiers:

• Paper 5: "The Elastic Vacuum" (Kriger, 2025) — Is continued by this upload
• Paper 6: "Connection of Vacuum Energy with Inflation" (Kriger, 2026a) — Is continued by this upload
• ResearchGate Paper 6: https://www.researchgate.net/publication/401965593 — Is supplemented by this upload
• Research Programme Invitation: https://interdisciplinary-research.institute/2026/03/11/research-program-invitation/ — Is part of this upload

Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics – Theory (hep-th)

Version: 2.0 (revised following peer review)

Authors: Kriger, Boris (ORCID: 0009-0001-0034-2903)

Affiliations: ¹ Information Physics Institute, Gosport, Hampshire, United Kingdom ² Institute of Integrative and Interdisciplinary Research, Toronto, Canada

Upload type: Publication / Preprint

Publication date: 2026-03-13

Description:

Paper 7 of 17 in the research programme "What If the Vacuum Gravitates Locally?"