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Cloud–Bulk Interaction Field Equations and the Geometric Origin of the Cosmological Parameter Λ

Al-Fadhli MB

2026

Abstract

Observations from a wide range of cosmological probes indicate the presence of a non-zero cosmological constant, Λ, commonly interpreted as a constant vacuum energy density. In the standard framework combining General Relativity and quantum field theory, quantum vacuum contributions enter the gravitational field equations as terms proportional to gμν. This produces the well-known discrepancy between the observationally inferred and theoretically predicted vacuum energy densities, referred to as the cosmological constant problem. In addition, recent analyses combining SNe Ia, H(z), BAO, LSS, BBN, and CMB data have found preferences of up to 4.2σ for a time-dependent cosmological parameter. Revised supernova photometric calibrations temper this tension to 3.2σ, yet even at this reduced significance the signal, read alongside the long-standing cosmological constant problem, calls into question the identification of Λ with a fixed vacuum energy density. The presented framework instead models the quantum vacuum as a dynamical background (Bulk) endowed with its own metric ˜gμν, while embedded astrophysical systems are described as localized manifolds (Clouds). The resulting interaction field equations reduce locally to the Einstein field equations in the fully synchronized Cloud–Bulk limit. In the unlocked cosmological regime, the equations demonstrate that the effective cosmological term emerges from the residual Cloud–Bulk synchronization, with the background Bulk curvature…

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