Space-Energy Duality: A Unified 4-Index Framework for Resolving the Cosmological Constant Problem

We present a comprehensive Space-Energy Duality Theory that fundamentally extends Einstein's general relativity through a rigorous 4-index tensor formulation, providing a natural resolution to the cosmological constant problem. Our framework introduces a dynamic cosmological parameter $\lambdaeff(x,t)$ that self-regulates through space-energy interactions, reducing the quantum field theory vacuum energy prediction by approximately 120 orders of magnitude (naive Planck-scale cut-off estimate) or 54 orders (using dimensional regularization in the Standard Model) to match astronomical observations. The theory predicts specific measurable phenomena: additional gravitational wave polarization modes with relative amplitudes of $(2.5 \pm 0.6) \times 10^{-3}$, dark energy density fluctuations of $(7.8 \pm 1.3) \times 10^{-4}$ on 100 Mpc scales, and modified black hole entropy $S = (A/4\lp^2)[1 + (0.21 \pm 0.04)(A/A_{\text{Pl}})^{-1/3}]$. We establish experimental protocols targeting LIGO-Virgo O5 detection capabilities, DESI Year-5 dark energy evolution measurements requiring $\delta w$ precision of $(4 \pm 1) \times 10^{-4}$, and laboratory quantum sensing experiments. Parameter constraints derived from Planck 2018 CMB data, LIGO O3 gravitational wave observations, and solar system tests yield: $\alpha = 1.0008 \pm 0.0012$, $\beta = 0.494 \pm 0.028$, and $\lambda = (2.8 \pm 0.9) \times 10^{-122}\lp^{-2}$. The framework maintains exact energy-momentum conservation, ensures causal propagation, and demonstrates computational validation against current cosmological observations with $\chi^2_{\text{red}} = 1.12 \pm 0.08$. This approach bridges classical general relativity and quantum gravity while offering experimentally testable pathways toward unified physics. Detailed derivations and numerical implementations are provided in Appendices~\ref{app:derivations} to~\ref{app:conclusion_summary} and the Supplementary Material~\cite{SuppMat}.