Estimating the amount of vorticity generated by cosmological perturbations in the early universe

TL;DR

This paper estimates the generation of vorticity in the early universe due to second-order cosmological perturbations, highlighting its significance on small scales for CMB observations.

Contribution

It provides a calculation of vorticity from first principles, considering non-adiabatic pressure perturbations in a radiation background, which was not thoroughly analyzed before.

Findings

Vorticity generated is significant on small scales.

The wave number dependence of vorticity power spectrum is characterized.

Implications for CMB experiments are discussed.

Abstract

We estimate the amount of vorticity generated at second order in cosmological perturbation theory from the coupling between first order energy density and non-adiabatic pressure, or entropy, perturbations. Assuming power law input spectra for the source terms, and working in a radiation background, we calculate the wave number dependence of the vorticity power spectrum and its amplitude. We show that the vorticity generated by this mechanism is non-negligible on small scales, and hence should be taken into consideration in current and future CMB experiments.