Topological defects and scalar field modes in cosmological backgrounds

TL;DR

This paper analyzes topological defects in higher-dimensional cosmological backgrounds, providing mode functions for scalar fields and exploring specific universes like de Sitter and Milne.

Contribution

It offers a comprehensive set of scalar mode functions in complex higher-dimensional backgrounds with topological defects, including special cases like cosmic strings and monopoles.

Findings

Mode functions expressed via Legendre functions for general backgrounds

Explicit solutions for de Sitter and Milne universes in various coordinate systems

Extension of scalar field analysis to higher-dimensional topological defects

Abstract

We study topological defects with a general structure in higher-dimensional cosmological backgrounds described by a set of angle deficit parameters. As special cases, they include higher-dimensional generalizations of cosmic strings and global monopoles. The corresponding complete set of mode functions is presented for a massive scalar field with a general curvature coupling parameter. For general scale factors and radial functions in the line element, the angular parts of the scalar modes are expressed in terms of associated Legendre functions. De Sitter and Milne universes are considered as examples of cosmological expansion. For the de Sitter bulk, we present the time-dependent parts of the mode functions in inflationary, hyperbolic, and global coordinates.