Dark Energy Density in Brane World

TL;DR

This paper explores a theoretical model where the tiny positive cosmological constant is explained by quantum zero point energy in a brane-world scenario, specifically within an AdS$_5$ spacetime with a dS$_4$ brane, aiming to match observed dark energy density.

Contribution

It introduces a calculation of dark energy density from zero point energies in an AdS$_5$ spacetime with a dS$_4$ brane, providing a potential explanation for the small positive cosmological constant.

Findings

Calculated dark energy density is smaller than observational value.

Assumption that AdS$_5$ radius matches observable universe's radius.

Discussed reasons for discrepancy between calculated and observed dark energy density.

Abstract

We present a possible explanation to the tiny positive cosmological constant under the frame of AdS$_5$ spacetime embedded by a dS$_4$ brane. We calculate the dark energy density by summing the zero point energy of massive scalar fields in AdS$_5$ spacetime. Under the assumption that the radius of AdS$_5$ spacetime is of the same magnitude as the radius of observable universe, the dark energy density in dS$_4$ brane is obtained, which is smaller than the observational value. The reasons are also discussed.