A hard-core lattice-gas model of the cosmological vacuum: thermodynamics, equation of state, and cohesive calibration to 𝛀𝚲

Abstract We construct an effective statistical-mechanical model of the cosmological vacuum based on a hard-core bosonic lattice gas defined on a discrete substrate. Each elementary cell of volume may host at most one excitation, producing a finite saturation density . From the grand canonical ensemble we derive a homogeneous equation of state combining a configurational packing pressure, which diverges as , with a low-density cohesive contribution controlled by a single coupling . In the cosmological branch , the equation of state reduces to , corresponding to an effective vacuum-energy density and equation-of-state parameter . Identifying the effective fluctuation temperature with the Gibbons–Hawking temperature of the asymptotic de Sitter background suppresses the packing contribution by a factor of order . Calibrating to the observed dark-energy density fixes , yielding for Planck 2018 parameters. The construction matches the homogeneous dark-energy sector of CDM once the cohesive coupling is calibrated to the observed vacuum-energy density, and provides a statistical-mechanical saturation ceiling for the substrate density. No gravitational dynamics is derived here; the paper is self-contained as a thermodynamic and statistical-mechanical proposal for the cosmological vacuum sector. Keywords: discrete spacetime; emergent vacuum; equation of state; lattice gas; hard-core bosons; cosmological constant problem; dark energy.