Observable vacuum energy is finite in expanding space

TL;DR

This paper proposes that in expanding space, only quantum modes within the observable volume contribute to vacuum energy, leading to a finite, gravity-consistent vacuum energy density that scales with the square of the Hubble parameter.

Contribution

It introduces a method to compute vacuum energy in expanding space by restricting modes to the observable patch, avoiding regularisation and renormalisation.

Findings

Vacuum energy density scales with the square of the Hubble parameter.

Finite volume acts as an infrared regulator, making calculations tractable.

Vacuum energy remains consistent with gravitational constraints.

Abstract

In this work I reason that in expanding space only those quantum modes contribute to the measured vacuum energy that do not transcend the observable volume. Since all quantised field modes have various observable consequences, when a gravitational horizon causally confines an observer to a finite volume quantised modes should be restricted to the observable patch to remain consistent with gravity. Within the observable patch of Friedmann-Lemaitre-Robertson-Walker (FLRW) space the vacuum expectation value of the energy-momentum tensor can be expressed as a sum over discrete field modes. Friedmann's first equation provides a straightforward ultraviolet cut-off allowing only a finite number of modes in the sum. The finite volume acts as an infrared regulator and the calculation of the vacuum energy density is tractable without regularisation and renormalisation. To test the validity of this idea I quantise a scalar field on an FLRW background and calculate its vacuum energy density in the vacuum dominated, conformal, holographic limit. In this limit I show that the quantum vacuum energy density scales with the square of the Hubble parameter, consistently with gravity. In this example quantum vacuum expands space while the horizon of the expanding space limits the energy density of the vacuum to the observed value.