The intergalactic space (IGS) has ideal conditions to test the weak but cumulative action that the electromagnetic (EM) zero-point field (ZPF) of ordinary quantum theory (QT), if conceived as a real field, may have on EM interacting particles. Recent results (classical stochastic and quantum) indicate that if the EM ZPF of ordinary QT is conceptually assimilated to a real random field, electrically polarizable particles perform a random walk in velocity space to ever-increasing translational kinetic energies. As the ZPF has a Lorentz-invariant energy density spectrum, statistically it keeps the same form and is homogeneous and isotropic in all inertial frames of reference. No velocity-dependent forces can hence appear on particles moving through the ZPF. Acceleration is thus possible in a high vacuum. The hierarchy of dissipation mechanisms for the accelerated ultrarelativistic protons in the IGS is established in detail. In the IGS outside superclusters cosmic expansion is the most significant dissipation mechanism. The previously derivedE −η particle energy spectrum is obtained except for a cut-off: cosmic expansion puts a drastic cut-off to the energy spectrum of ZPF accelerated particles in the IGS out-side clusters or superclusters. This cut-off does not appear for CR primaries confined to the magnetic cavities of clusters or superclusters. When this confinement is effective, the ZPF acceleration may still be as relevant a CR acceleration mechanism as previously contended. The possible relevance of the ZPF in energizing the intergalactic medium (IGM) is briefly discussed. As it has recently been shown that electrons are not accelerated by the ZPF, electrons can only receive energy from the proton component of the IGM plasma and should display an approximately Maxwellian distribution. This could not occur, would electrons absorb energy directly from the ZPF. In that case they would display the Lorentz-invariant distribution. The electron component loses energy mainly by thermal bremsstrahlung or by inverse Compton collisions with the 2.7 K photons depending on the assumed number density of IGS electrons. The X-ray emission of the proton component can be dismissed in comparison with that of the electrons, despite the usual higher energies of protons in their distribution which is not Maxwellian. The relevance of the ZPF acceleration model for explaining the observed X-ray background is preliminarily discussed. The inherent thermodynamic limitations of the model are also briefly outlined.