The zero point energy and gravitation

TL;DR

This paper explores the relationship between vacuum fluctuations, gravity, and dark energy, proposing a cutoff based on gravitational radius that affects the vacuum's equation of state at different length scales.

Contribution

It introduces a novel approach linking vacuum energy, gravity, and a natural cutoff, revealing scale-dependent equations of state and mass independence in certain regimes.

Findings

Below 1 mm, vacuum pressure is one third of energy density, similar to dark matter.

Above 1 mm, the vacuum behaves like dark energy with negative pressure.

Vacuum energy becomes infinite as Newton's constant approaches zero.

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 $L = 1 mm$ the pressure $sigma$ is one third of the energy density $epsilon$, as for dark matter, but above $1 mm$ the equation of state is $sigma = -(epsilon)$ (dark energy). In the case of a massive field, W does not depend on the mass of the field for $L<<1 mm$ but for $L>>1 mm$ it does not depend on the Planck constant. 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.