Dark Energy as Closure-Density Imbalance
In standard cosmology, the expansion of the Universe is described using the Hubble parameter and a cosmological constant $\Lambda$:
$$H^2 = \frac{8\pi G}{3}\rho + \frac{\Lambda c^2}{3}$$
In this framework, $\Lambda$ is introduced as an independent parameter to account for accelerated expansion.
QMU / APM Expansion Law
In the Aether Physics Model, the expansion rate is derived from first principles:
$$H = F_q\,\alpha_a^{4/5}\sqrt{\frac{8\pi}{3}}$$
Squaring gives:
$$H^2 = F_q^2\,\alpha_a^{8/5}\,\frac{8\pi}{3}$$
This has the same structural form as standard cosmology, but all terms are derived.
Definition of Terms
Quantum frequency:
$$F_q = \frac{c}{\lambda_C}$$
Aether fine-structure parameter:
$$\alpha_a = \frac{e^2}{8\pi e_a^2}$$
Closure-density term:
$$\Omega_{cl} = \alpha_a^{8/5}$$
Closure Measure
The closure exponent arises from:
$$D_{cl} = \frac{N_{arc}}{N_{con}} = \frac{8}{5}$$
Thus:
$$\Omega_{cl} = \alpha_a^{D_{cl}} = \alpha_a^{8/5}$$
Isotropic Closure Factor
Total angular measure:
$$\int_{S^2} d\Omega = 4\pi$$
Volumetric normalization:
$$\Gamma_{vol} = \frac{4\pi}{3}$$
Bidirectional closure:
$$\Gamma_{iso} = 2\Gamma_{vol} = \frac{8\pi}{3}$$
Interpretation
In this framework, the phenomenon commonly attributed to dark energy is not a separate energy component. Instead, it is the geometric projection of closure-density imbalance.
The expansion law becomes:
$$H^2 = F_q^2\,\Omega_{cl}\,\Gamma_{iso}$$
This replaces the need for an independently specified cosmological constant.
Numerical Result
Using QMU values:
$$\alpha_a \approx 2.0345684859\times 10^{-48}$$
$$F_q \approx 1.235589965\times 10^{20}\,s^{-1}$$
We obtain:
$$H \approx 2.5131\times 10^{-18}\,s^{-1}$$
$$H_0 \approx 77.55\,km\,s^{-1}\,Mpc^{-1}$$
Conclusion
Dark energy, in the Aether Physics Model, is reinterpreted as closure-density imbalance. The quantity that plays the role of $\Lambda$ is derived from geometry and topology rather than introduced as an independent constant.