Cosmological perturbation theory lecture notes

In cosmological perturbation theory we have chosen the background coordinates to respect its homogeneity property, which gives us unique slicing of the spacetime into homogeneous t = const. spacelike slices.
Thus we do not want to change this slicing.

9In practice, they are just functions of the four coordinates, , x, y, z, of the background spacetime, and since in cosmological perturbation theory the time slicing of the background spacetime is xed, and since we here just consider at background spacetimes, the perturbations become just elds in Euclidean space that evolve in time.

They are responsible for the formation of structure in the universe from small initial perturbations.
Vector perturbations couple to rotational velocity perturbations in the cosmic uid.
They tend to decay in an expanding universe, and are therefore probably not important in cosmology.
We have done all of the above in a xed gauge.