Vacuum Energy, the Cosmological Constant and Compact Extra Dimensions: Constraints from Casimir Effect Experiments

TL;DR

This paper analyzes how a universe with a compact extra dimension and a vacuum energy cutoff affects the Casimir force, finding that the predicted repulsive force contradicts experimental observations, thus challenging vacuum energy as the cosmological constant.

Contribution

It provides a detailed calculation of the Casimir force in models with extra dimensions and vacuum energy cutoff, showing inconsistencies with experimental results.

Findings

Casimir force becomes repulsive at small separations for certain parameters

Predicted critical separation exceeds experimental limits

Vacuum energy with cutoff cannot account for the cosmological constant

Abstract

We consider a universe with a compact extra dimension and a cosmological constant emerging from a suitable ultraviolet cutoff on the zero point energy of the vacuum. We derive the Casimir force between parallel conducting plates as a function of the following scales: plate separation, radius of the extra dimension and cutoff energy scale. We find that there are critical values of these scales where the Casimir force between the plates changes sign. For the cutoff energy scale required to reproduce the observed value of the cosmological constant, we find that the Casimir force changes sign and becomes repulsive for plate separations less than a critical separation $d_0=0.6mm$, assuming a zero radius of the extra dimension (no extra dimension). This prediction contradicts Casimir experiments which indicate an attractive force down to plate separations of $100nm$. For a non-zero extra dimension radius, the critical separation $d_0$ gets even larger than $0.6mm$ and remains inconsistent with Casimir force experiments. We conclude that with or without the presence of a compact extra dimension, vacuum energy with any suitable cutoff can not play the role of the cosmological constant.