Cosmological Constant of the $(p+1)$-Dimensional World, Embedded in the $d$-Dimensional Bulk Space

TL;DR

This paper investigates how the cosmological constant of a lower-dimensional universe embedded in higher-dimensional space can be explained through scalar field dynamics and parameter adjustments, considering both positive and negative bulk cosmological constants.

Contribution

It introduces a model linking the cosmological constant of a lower-dimensional world to scalar field dynamics in a higher-dimensional bulk with compact extra dimensions.

Findings

Tiny cosmological constant achieved via scalar field dynamics.

Dirac quantization conditions derived for the cosmological constants.

Analysis includes both positive and negative bulk cosmological constant cases.

Abstract

In this manuscript we study the cosmological constant of a $(p+1)$-dimensional world, which lives in the higher dimensional bulk space. We assume the extra dimensions are compact on tori. We consider two cases: positive and negative bulk cosmological constant. It is pointed out that the tiny cosmological constant of our world can be obtained by the dynamics of a scalar field and adjusting the parameters of the model. The cosmological constant of the dual world also will be discussed. We obtain the Dirac quantization of these cosmological constants.