The cosmological vector modes from a monochromatic primordial power spectrum

TL;DR

This paper systematically investigates higher order cosmological vector modes generated by scalar perturbations, finding that third order vector modes can be produced by a monochromatic primordial spectrum, with dominance of third order modes sourced by second order scalars.

Contribution

It provides explicit expressions for second and third order vector mode correlations and demonstrates the generation of third order modes from a monochromatic primordial spectrum.

Findings

Second order vector modes do not exist for a monochromatic spectrum.

Third order vector modes can be generated and dominate the correlation functions.

Third order modes sourced by second order scalars are the main contribution.

Abstract

The cosmological background of higher order vector modes can be generated by the first order scalar perturbations. We investigate the second order and the third order vector modes systematically. The explicit expressions of two point functions $\langle V^{(n),\lambda}V^{(n),\lambda'} \rangle$$\left(n=2,3\right)$ and power spectra corresponded are presented. In the case of a monochromatic primordial power spectrum, the second order vector modes do not exist. However, the third order vector modes can be generated by a monochromatic primordial power spectrum. And it is found that the third order vector modes sourced by the second order scalar perturbations dominate the two point function $\langle V^{(3),\lambda}V^{(3),\lambda'} \rangle$ and power spectrum corresponded.