Operational holographic approach to vacuum energy and cosmic acceleration in the HDOV framework: master equation, functional accessibility and cosmological consequences

The so-called vacuum catastrophe—the ∼10^122 discrepancy between the zero-point energy density predicted by quantum field theory and the effective cosmological constant inferred from observations—is addressed here through a strictly operational and holographic framework consistent with General Relativity and Bekenstein–Hawking–type information bounds. Within the HDOV approach, a scalar field of functional accessibility, η_p, encodes the fraction of the state space associated with a physical mode that remains operationally accessible to a macroscopic observer in a given environment. When η_p is incorporated into a covariant effective action, one obtains an HDOV master equation for the observable field Ψ that, in the WKB regime, leads to an exponential attenuation of the accessible amplitude along the ray.

In this work the same accessibility mechanism is applied to high-energy modes of the quantum vacuum, modeled by a smooth spectral weight W_η(k) in momentum space, holographically regulated instead of imposing ad hoc hard cut-offs. We formulate an HDOV Holographic Projection Theorem showing that, under accessibility and holographic saturation hypotheses, the accessible vacuum energy density is naturally constrained to be of the order of the cosmological constant, and that this lower bound does not depend on the detailed shape of W_η(k). The construction is illustrated with explicit numerical examples of smooth spectral weights compared with sharp effective cut-offs, calibrated with current cosmological parameters, emphasizing that the proposal is operational and holographic: it regulates the accessible sector of the vacuum without claiming a complete microphysical theory of vacuum energy.