Weighing the Vacuum Energy

TL;DR

This paper explores the properties of vacuum energy in various spacetime geometries, revealing relationships between energy scales and examining how different theories of gravity influence vacuum energy's gravitational effects.

Contribution

It provides new calculations of vacuum energy in flat and curved spacetimes, and shows that in Unimodular Gravity vacuum energy does not contribute to gravity.

Findings

Energy at radius R relates simply to energy at l_s^2 / R

Vacuum energy in curved spacetime depends on the gravity theory

In Unimodular Gravity, vacuum energy does not gravitate

Abstract

We discuss the weight of vacuum energy in various contexts. First, we compute the vacuum energy for flat spacetimes of the form $\mathbb{T}^3 \times \mathbb{R}$, where $\mathbb{T}^3$ stands for a general 3-torus. We discover a quite simple relationship between energy at radius $R$ and energy at radius $\frac{l_s^2}{ R}$. Then we consider quantum gravity effects in the vacuum energy of a scalar field in $\mathbb{M}_3 \times S^1$ where $\mathbb{M}_3$ is a general curved spacetime, and the circle $S^1$ refers to a spacelike coordinate. We compute it for General Relativity and generic transverse {\em TDiff} theories. In the particular case of Unimodular Gravity vacuum energy does not gravitate.