In the context of the cosmological perturbation theory, perturbations can be decomposed into the scalar, vector, and tensor modes. Current observations strongly support only the scalar mode. It is known that the vector mode does not arise from the linear perturbation theory in the standard cosmology.
In this talk, I will introduce the second-order vector mode, which is inevitably generated in the standard cosmology. I also show the way to observe the vector-mode signature. Finally, I will mention a role of the second-order vector mode in observational cosmology.