Vacuum energy in the effective field theory of general relativity with a scalar field

TL;DR

This paper shows that in an effective field theory of gravity with a scalar field, the cosmological constant must be fixed to ensure zero vacuum energy, supporting a consistent theory with massless gravitons.

Contribution

It extends previous two-loop calculations to include scalar field self-interactions, confirming the vanishing vacuum energy condition in a broader effective field theory framework.

Findings

Vanishing vacuum energy at two-loop order with scalar fields included.

The cosmological constant is fixed by consistency conditions to ensure zero vacuum energy.

Supports the idea of a consistent effective field theory with massless gravitons.

Abstract

A consistency condition of general relativity as an effective field theory in Minkowskian background uniquely fixes the value of the cosmological constant. In two-loop calculations, including the interaction of gravitons with matter fields, it has been shown that this value of the cosmological constant leads to vanishing vacuum energy, under the assumption that the energy-momentum tensor of the gravitational field is given by the pseudotensor of Landau-Lifshitz's classic textbook. Here, we demonstrate that this result also holds when the self-interaction of a scalar field is taken into account. That is, our two-loop-order calculation suggests that in an effective field theory of metric and scalar fields, one arrives at a consistent theory with massless gravitons if the cosmological constant is fixed from the condition of vanishing vacuum energy. Vice versa, imposing the consistency condition in Minkowskian background leads to a vanishing vacuum energy.