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Scalar perturbations in a flat universe are represented by
,which are the eigenfunctions
of the Laplacian operator
and their spatial derivatives. For example,
vector and symmetric tensor quantities such as velocities and
stresses based on scalar perturbations
can be constructed as
Since , velocity fields
based on scalar perturbations are irrotational.
Notice that Q(0)= G00, ni Qi(0)= G10 and
,where the coordinate system is defined by .From the orthogonality of the spherical harmonics, it follows
that scalars generate only m=0 fluctuations in the radiation.