Spectral Hierarchy of the Cosmological Constant, Mukhanov–Sasaki Derivation,Scale Separation,and Primordial Observational Signatures
Fuente:
Zenodo
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Recurso digital |
| Lenguaje: | inglés |
| Publicado: |
Zenodo
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866901994734616576 |
|---|---|
| author | Rojas Fedorow Dimitri Andrés |
| author_facet | Rojas Fedorow Dimitri Andrés |
| contents | <p>This is Paper 2 of a three-part program on the spectral selection of the cosmological constant.</p> <p><strong>Paper 1</strong> (<a href="https://doi.org/10.5281/zenodo.18736246" target="_blank" rel="noopener noreferrer">https://doi.org/10.5281/zenodo.18736246</a>) established that the cosmological constant Λ emerges as the ground-state eigenvalue of a Wheeler–DeWitt effective potential derived from quantum and instanton contributions. That paper identified two open problems: the semi-quantitative nature of the predicted primordial power spectrum modification and the absence of a derivation connecting the quantum structure to the Standard Model electromagnetic sector.</p> <p><strong>This paper (Paper 2)</strong> addresses the first of these problems. Starting from the full cosmological action with Λ treated as a dynamical quantum degree of freedom, the spectral structure Λₙ = Λ₀ + nΔΛ is propagated through the Friedmann equations into the Mukhanov–Sasaki equation for scalar curvature perturbations. The key results are:</p> <ul> <li> <p>A rigorous derivation of how the Wheeler–DeWitt ground-state zero-point fluctuations act as a periodic perturbation to the inflationary dynamics.</p> </li> <li> <p>The analytical demonstration that this perturbation generates a log-periodic modulation of the primordial curvature power spectrum, with an amplitude A ∼ 10⁻³ and a frequency ω_Λ/H ∼ 10–100, both derivable from the parameters of the effective potential introduced in Paper 1.</p> </li> <li> <p>The identification of a critical scale separation between the late-universe vacuum energy Λ₀ and the inflationary Hubble scale H_inf, resolving a potential confusion in preliminary treatments.</p> </li> <li> <p>A spectral hierarchy showing that each Wheeler–DeWitt eigenstate produces a distinct primordial spectrum, linking the quantum structure of Λ to a cosmological hierarchy of possible universes.</p> </li> <li> <p>Observational predictions that distinguish this mechanism from other models such as axion monodromy inflation: suppressed non-Gaussianity (f_NL ∼ 10⁻⁶), an oscillatory scale-dependent correction to the spectral index n_s of order 10⁻², and consistency with current bounds from Planck, ACT, and SPT. The predicted amplitude is within reach of next-generation experiments like CMB-S4.</p> </li> <li> <p>An explicit statement of the most critical open problem: the conversion of the rescaled Wheeler–DeWitt oscillation frequency to physical units, which would sharpen the amplitude prediction from a self-consistency argument to a first-principles result.</p> </li> </ul> <p><strong>Paper 3</strong> (in preparation) will embed this spectral selection in a cyclic cosmological framework, explaining why the universe is in the ground state n = 0 and fixing the oscillation phase φ₀ through entropy transfer between cycles.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19056166 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Spectral Hierarchy of the Cosmological Constant, Mukhanov–Sasaki Derivation,Scale Separation,and Primordial Observational Signatures Rojas Fedorow Dimitri Andrés Wheeler–DeWitt equation Mukhanov–Sasaki primordial power spectrum cosmological constant quantisation inflationary perturbations CMB oscillations spectral index non-Gaussianity scale separation <p>This is Paper 2 of a three-part program on the spectral selection of the cosmological constant.</p> <p><strong>Paper 1</strong> (<a href="https://doi.org/10.5281/zenodo.18736246" target="_blank" rel="noopener noreferrer">https://doi.org/10.5281/zenodo.18736246</a>) established that the cosmological constant Λ emerges as the ground-state eigenvalue of a Wheeler–DeWitt effective potential derived from quantum and instanton contributions. That paper identified two open problems: the semi-quantitative nature of the predicted primordial power spectrum modification and the absence of a derivation connecting the quantum structure to the Standard Model electromagnetic sector.</p> <p><strong>This paper (Paper 2)</strong> addresses the first of these problems. Starting from the full cosmological action with Λ treated as a dynamical quantum degree of freedom, the spectral structure Λₙ = Λ₀ + nΔΛ is propagated through the Friedmann equations into the Mukhanov–Sasaki equation for scalar curvature perturbations. The key results are:</p> <ul> <li> <p>A rigorous derivation of how the Wheeler–DeWitt ground-state zero-point fluctuations act as a periodic perturbation to the inflationary dynamics.</p> </li> <li> <p>The analytical demonstration that this perturbation generates a log-periodic modulation of the primordial curvature power spectrum, with an amplitude A ∼ 10⁻³ and a frequency ω_Λ/H ∼ 10–100, both derivable from the parameters of the effective potential introduced in Paper 1.</p> </li> <li> <p>The identification of a critical scale separation between the late-universe vacuum energy Λ₀ and the inflationary Hubble scale H_inf, resolving a potential confusion in preliminary treatments.</p> </li> <li> <p>A spectral hierarchy showing that each Wheeler–DeWitt eigenstate produces a distinct primordial spectrum, linking the quantum structure of Λ to a cosmological hierarchy of possible universes.</p> </li> <li> <p>Observational predictions that distinguish this mechanism from other models such as axion monodromy inflation: suppressed non-Gaussianity (f_NL ∼ 10⁻⁶), an oscillatory scale-dependent correction to the spectral index n_s of order 10⁻², and consistency with current bounds from Planck, ACT, and SPT. The predicted amplitude is within reach of next-generation experiments like CMB-S4.</p> </li> <li> <p>An explicit statement of the most critical open problem: the conversion of the rescaled Wheeler–DeWitt oscillation frequency to physical units, which would sharpen the amplitude prediction from a self-consistency argument to a first-principles result.</p> </li> </ul> <p><strong>Paper 3</strong> (in preparation) will embed this spectral selection in a cyclic cosmological framework, explaining why the universe is in the ground state n = 0 and fixing the oscillation phase φ₀ through entropy transfer between cycles.</p> |
| title | Spectral Hierarchy of the Cosmological Constant, Mukhanov–Sasaki Derivation,Scale Separation,and Primordial Observational Signatures |
| topic | Wheeler–DeWitt equation Mukhanov–Sasaki primordial power spectrum cosmological constant quantisation inflationary perturbations CMB oscillations spectral index non-Gaussianity scale separation |
| url | https://doi.org/10.5281/zenodo.19056166 |