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In this special issue article, based on the talk with the same title insession B5 (Theoretical and Mathematical Cosmology) at GR19, we review the caseof vorticity generation in cosmology using cosmological perturbation theory. Weshow that, while at linear order the vorticity evolution equation has no sourceterm in the absence of anisotropic stress, at second order vorticity is sourcedby gradients in entropy and energy density perturbations. We then present someestimates for the magnitude and scale dependence of the vorticity powerspectrum using simple input power spectra for the energy density and entropyperturbations. Finally, we close with possible directions for future workfollowed by some hints toward the observational importance of the vorticity sogenerated, and the possibility of primordial magnetic field generation.

Can cosmological perturbations produce early universe vorticity?