The cosmological background of vector modes

TL;DR

This paper studies the generation and properties of second-order vector modes from density perturbations in cosmology, highlighting their small amplitude and potential observational effects.

Contribution

It clarifies the generation mechanism of vector modes at second order and extends previous results with detailed calculations of their spectrum and energy density.

Findings

Vector modes are about 1% of first-order scalars on small scales.

Generated vector modes can influence the Sachs-Wolfe effect, redshift-space distortions, and weak lensing.

No vorticity is produced at second order in the fluid.

Abstract

We investigate the spectrum of vector modes today which is generated at second order by density perturbations. The vector mode background that is generated by structure formation is small but in principle it contributes to the integrated Sachs-Wolfe effect, to redshift-space distortions and to weak lensing. We recover, clarify and extend previous results, and explain carefully why no vorticity is generated in the fluid at second order. The amplitude of the induced vector mode in the metric is around 1% that of the first-order scalars on small scales. We also calculate the power spectrum and the energy density of the vector part of the shear at second order.