The Cutoff Ladder: Zero-Point Energy Density at Eight Scales and the Fraction That Would Have to Survive at Each

The zero-point energy of a quantum field depends on where its mode sum is cut off, yet the density that gravitates in the observed universe is fixed. This paper evaluates the standard integral, which gives a density of Lambda^4/(16 pi^2) per bosonic degree of freedom, at eight cutoffs from the Planck scale to the neutrino mass scale, and compares each value with an observed vacuum density of 2.52 x 10^-47 GeV^4 derived from a Hubble constant of 67.4 km/s/Mpc and a dark-energy fraction of 0.685. The Planck-scale value exceeds the observed density by 120.7 orders of magnitude; the electroweak value exceeds it by 54.0 orders; even a cutoff at the QCD scale leaves an excess of 41.6 orders. Only a cutoff near the neutrino scale approaches the target. The computation is a stated-assumption calculation, not a measurement.