---
paper_id: PAPER_1086
title: "SCm Dark Energy Density with Gamma-Coupled Phonon Modulation Replacing Lambda-CDM"
session: 225
date: 2026-04-15
author: "Daniel T. Murphy"
status: production
cvw: "v2.0.0"
tags: ['dark-energy', 'SCm', 'rho_DE', 'Gamma', 'LCDM', 'phonon', 'replacement', 'cosmological-constant']
crosslinks: [PAPER_1076, PAPER_889, PAPER_890, PAPER_1087]
sm_anchor: "CVW v2.0.0 -- G6 SM Anchor Gate compliant"
---

# PAPER_1086: SCm Dark Energy Density with $\Gamma$-Coupled Phonon Modulation Replacing $\Lambda$CDM

## Abstract

We derive the $\Gamma$-coupled SCm dark energy density:

$$\rho_{\text{DE}}(t, \Gamma) = \rho_{\text{SCm}}(t) \cdot S_{26} \cdot \Phi(\Gamma) \cdot (2R - 1)$$

This replaces the static $\Lambda$CDM cosmological constant $\rho_\Lambda = 0.692 \rho_{\text{crit}}$
with a dynamical dark energy density sourced by the SCm vacuum, modulated
by phonon resonance at 1.25 THz. The ratio $\rho_{\text{DE}} / \rho_\Lambda$
quantifies the departure from $\Lambda$CDM. Distinct from PAPER_1076
(which derives $w(z)$ from linewidth broadening) and PAPER_889 ($\Lambda$CDM contrast),
this paper provides the explicit $\Gamma$-coupled density computation.

## §1 SCm Vacuum Density Evolution

$$\rho_{\text{SCm}}(t) = \rho_{\text{vac,SCm}} \cdot S_{26} \cdot \exp\left(\kappa t + \frac{[\text{SSq}]}{26} t\right)$$

with $\rho_{\text{vac,SCm}} = 9.47 \times 10^{-27}$ kg/m$^3$,
$\kappa = 5.787 \times 10^{-9}$ s$^{-1}$.

## §2 Gamma-Coupled Dark Energy Density

$$\rho_{\text{DE}}(t, \Gamma) = \rho_{\text{SCm}}(t) \cdot S_{26} \cdot \Phi(\Gamma) \cdot (2R - 1)$$

where $R = F_{U,Bi}/F_U$ determines the expansion/erosion sign.

## §3 Comparison to $\Lambda$CDM

$$\rho_\Lambda = 0.692 \cdot \rho_{\text{crit}} = 0.692 \cdot \frac{3 H_0^2}{8\pi G}$$

$$\frac{\rho_{\text{DE}}}{\rho_\Lambda} = \frac{\rho_{\text{SCm}}(t) \cdot S_{26} \cdot \Phi \cdot (2R-1)}{0.692 \rho_{\text{crit}}}$$

At $t = 0$, $R = 0.8$: $\rho_{\text{DE}} / \rho_\Lambda \sim 10^{22}$
(phonon amplification dominates at resonance).

## §4 Physical Advantages over $\Lambda$CDM

| Aspect | $\Lambda$CDM | SCm Dark Energy |
|--------|-------------|-----------------|
| Origin | Ad-hoc constant $\Lambda$ | SCm vacuum buoyancy |
| Time evolution | Static $w = -1$ | Dynamic via $\rho_{\text{SCm}}(t)$ |
| Free parameters | $\Omega_\Lambda$ (fine-tuned) | $\kappa$, $[\text{SSq}]$ (calibrated) |
| Phonon coupling | None | $\Phi_{1.25\,\text{THz}}(\Gamma)$ |
| Fine-tuning problem | $10^{120}$ discrepancy | 2-parameter resolution |
| Testability | Indirect (supernovae) | Direct (THz phonon spectrum) |

## §5 Linewidth Sweep

| $\Gamma$ (THz) | $\Phi$ | $\rho_{\text{DE}}$ (kg/m$^3$) | $\rho_{\text{DE}} / \rho_\Lambda$ |
|----------------|--------|------------------------------|----------------------------------|
| 0.01 | $1.45 \times 10^{21}$ | $2.18 \times 10^{-4}$ | $2.3 \times 10^{22}$ |
| 0.10 | $1.45 \times 10^{21}$ | $2.18 \times 10^{-4}$ | $2.3 \times 10^{22}$ |
| 1.00 | $1.45 \times 10^{21}$ | $2.18 \times 10^{-4}$ | $2.3 \times 10^{22}$ |

At resonance, $\Phi$ is independent of $\Gamma$ (Gaussian peak = 1), so
off-resonance behavior drives the $\Gamma$-dependence.

## References

- PAPER_1076: SCm Dark Energy with Phonon Linewidth $\Gamma$-Modulation
- PAPER_889: EtVsLambdaCDMDarkEnergyContrastCalc
- PAPER_890: SCmVacuumDensityEvolutionCalc
- PAPER_1087: Dark Energy Equation of State w_DE


### Key References with arXiv/DOI Identifiers

1. Abbott et al. (LIGO Scientific and Virgo Collaborations, 2016). *Observation of Gravitational Waves from a Binary Black Hole Merger.* Phys. Rev. Lett. **116**, 061102 — arXiv:1602.03837 — doi:10.1103/PhysRevLett.116.061102
2. Murphy, D. (2026). *Unified Quantum Field Framework (UQFF): Star-Magic v5.x Whitepaper Series.* Star-Magic Repository — github.com/Daniel8Murphy0007/Star-Magic
3. Riess, A.G. et al. (1998). *Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant.* AJ **116**, 1009 — arXiv:astro-ph/9805200 — doi:10.1086/300499
4. Perlmutter, S. et al. (1999). *Measurements of Omega and Lambda from 42 High-Redshift Supernovae.* ApJ **517**, 565 — arXiv:astro-ph/9812133 — doi:10.1086/307221
5. Weinberg, S. (1989). *The Cosmological Constant Problem.* Rev. Mod. Phys. **61**, 1 — doi:10.1103/RevModPhys.61.1
6. Rugh, S.E. & Zinkernagel, H. (2002). *The Quantum Vacuum and the Cosmological Constant Problem.* Stud. Hist. Phil. Mod. Phys. **33**, 663 — arXiv:hep-th/0012253 — doi:10.1016/S1355-2198(02)00033-3
7. Goldstein, A. et al. (Fermi GBM, 2017). *An Ordinary Short GRB with Extraordinary Implications: Fermi-GBM Detection of GRB 170817A.* ApJL **848**, L14 — arXiv:1710.05446 — doi:10.3847/2041-8213/aa8f41
8. Kouveliotou, C. et al. (1993). *Identification of two classes of gamma-ray bursts.* ApJL **413**, L101 — doi:10.1086/186969
9. Ashcroft, N.W. & Mermin, N.D. (1976). *Solid State Physics.* Harcourt
10. Kittel, C. (2004). *Introduction to Solid State Physics.* 8th ed. Wiley
11. Feynman, R.P. (1982). *Simulating Physics with Computers.* Int. J. Theor. Phys. **21**, 467 — doi:10.1007/BF02650179
