Towards Kaluza-Klein Dark Matter on Nilmanifolds

TL;DR

This paper investigates the spectrum of scalar fields on nilmanifolds, a class of negatively curved spaces, and explores their potential as dark matter candidates within a Kaluza-Klein framework.

Contribution

It provides analytical results for the field spectrum on nilmanifolds and applies these findings to propose a stable dark matter candidate.

Findings

Analytical spectrum results for scalar fields on nilmanifolds

Validation of numerical methods against analytical solutions

Identification of a stable massive state as a dark matter candidate

Abstract

We present a first study of the field spectrum on a class of negatively-curved compact spaces: nilmanifolds or twisted tori. This is a case where analytical results can be obtained, allowing to check numerical methods. We focus on the Kaluza-Klein expansion of a scalar field. The results are then applied to a toy model where a natural Dark Matter candidate arises as a stable massive state of the bulk scalar.