Resolving the Cosmological Constant Problem via Dual-Scale Geometric Holography

Abstract

The most severe discrepancy in modern theoretical physics is the vacuum catastrophe—a staggering $10^{120}$ order-of-magnitude gap between the vacuum zero-point energy density calculated by classical quantum field theory and the dark energy density observed astronomically. Based on a dimensionless dual-geometric model $a(x) = 1/x^2 - x^2$, this paper reveals that this discrepancy is not a naturalness problem requiring fine-tuning, but rather an exact algebraic identity that holds inevitably under dual geometric scales: $\rho_{\text{crit}}/\rho_P = \frac{3}{8\pi}(l_p/L_H)^2$. Through holographic projection from the microscopic quantum scale onto the macroscopic Hubble boundary, the vacuum zero-point energy is suppressed and diluted by the maximum number of states on the holographic screen $N \approx 10^{120}$, naturally decaying to the observed value. This geometric mechanism not only resolves the $10^{120}$ divergence catastrophe, but also derives a tracking response wherein the dark energy density dynamically decays with cosmic expansion ($\rho_{\text{vac}} \propto 1/L_H^2$), aligning seamlessly with recent observational results from leading surveys like DESI.