Vacuum Polarization in an Anti-de Sitter Space as an Origin for a Cosmological Constant in a Brane World

TL;DR

This paper proposes that vacuum polarization effects in a five-dimensional anti-de Sitter space can naturally generate a small cosmological constant on a four-dimensional brane, explaining its observed tiny value.

Contribution

It introduces a model where vacuum polarization in AdS space accounts for the cosmological constant's smallness in a brane world scenario.

Findings

The model predicts a small positive cosmological constant consistent with observations.

It suggests testable gravity experiments at sub-millimeter scales.

The framework links quantum field effects in extra dimensions to cosmological phenomena.

Abstract

In this Letter we show that the vacuum polarization of quantum fields in an anti-de Sitter space naturally gives rise to a small but nonzero cosmological constant in a brane world living in it. To explain the extremely small ratio of mass density in the cosmological constant to the Planck mass density in our universe (\approx 10^{-123}) as suggested by cosmological observations, all we need is a four-dimensional brane world (our universe) living in a five-dimensional anti-de Sitter space with a curvature radius r_0 \sim 10^{-3}cm and a fundamental Planck energy M_P \sim 10^9 GeV, and a scalar field with a mass m \sim r_0^{-1}\sim 10^{-2}eV. Probing gravity down to a scale \sim 10^{-3}cm, which is attainable in the near future, will provide a test of the model.