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

We estimate the amount of vorticity generated at second order in cosmological perturbation theory from the coupling between first order energy density and nonadiabatic 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 cosmic microwave background experiments.

Figure 1

Plots of $I(k)$ for the illustrative choice of $k_c=10$.