Brane-vector dark matter and its connection to inflation and primordial gravitational waves

The scalar mode describing the fluctuation of the 3-brane (the observable universe) in a five-dimensional bulk spacetime compactified on a circle is absorbed by the Kaluza-Klein U(1) gauge field, leading to a massive brane-vector living on the 3-brane. The brane-vector can be responsible for dark matter because it is odd under a Z2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\textrm{Z}_2$$\end{document} symmetry, neutral under the Standard Model (SM) symmetries, and couples extremely weak to the SM particles due to its gravitational origin. Interestingly, the brane-vector dark matter could leave particular imprints on the cosmic microwave background (CMB) and the primordial gravitational waves. Hence, the precise measurements of the CMB and the observations of the primordial gravitational waves generated during inflation can provide a potential way to probe the extra-dimensions and branes which are the main ingredients of string/M theory.