On a gravitational cutoff for the vacuum energy

Abstract

A possible connection between the energy W of the vacuum fluctuations of quantum fields and gravity in "empty space" is conjectured in this paper using a natural cutoff of high momenta with the help of the gravitational radius of the vacuum region considered. We found that below some "critical" length L = 1mm the pressure σ is one third of the energy density ε, but above 1 mm the equation of state is σ = −ε as for dark energy). In the case of a massive field, W does not depend on the mass of the field for L << 1mm but for L >> 1mm it does not depend on . In addition, when the Newton constant tends to zero, W becomes infinite. The energy density is also a function of the volume V of the vacuum region taken into account.