Cosmological Constant from Horizon Entropy

"The vacuum is not heavy. Dark Energy is simply the information pressure on the cosmic horizon."

Objective

To solve the Cosmological Constant Problem (the 120-order-of-magnitude discrepancy between QFT prediction and observation) by re-deriving $\Lambda$ as a holographic surface term rather than a bulk volumetric energy.

1. The Hypothesis: Holographic Dark Energy (HDE)

Standard QFT assumes vacuum energy scales with volume ($L^3$), leading to $\rho_{vac} \sim M_{pl}^4$ (Catastrophe). We hypothesize that in a TARDIS universe, the energy density is saturated by the Bekenstein-Hawking Entropy of the horizon ($L^2$).

$$ \rho_{\Lambda} \approx \frac{3 c^2 M_p^2}{8 \pi L^2} $$ Where $L$ is the Hubble Horizon ($R_H \approx 1.37 \times 10^{26}$ m).

2. Calculation Results

We performed the calculation (simulation/holographic_lambda.py) using Planck 2018 data ($H_0 = 67.4$ km/s/Mpc).

Model	Prediction ($\rho_{vac}$)	Discrepancy
Standard QFT	$5.1 \times 10^{96} \text{ kg/m}^3$	$\sim 10^{123}$ (Catastrophe)
Observation	$5.8 \times 10^{-27} \text{ kg/m}^3$	-
Holographic (TARDIS)	$8.5 \times 10^{-27} \text{ kg/m}^3$	None (Ratio 1.46)

3. Conclusion

The vacuum catastrophe is an artifact of assuming the universe has infinite degrees of freedom in the bulk. When we apply the Holographic Principle (degrees of freedom proportional to Surface Area), the predicted energy density matches Dark Energy naturally. $\Lambda$ is not a substance. It is a boundary condition.

Files

• simulation/: Python scripts to calculate HDE.
• docs/: Theory papers.