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Scalar perturbations in a flat universe are represented by
plane waves
,which are the eigenfunctions
of the Laplacian operator

| |
(18) |

and their spatial derivatives. For example,
vector and symmetric tensor quantities such as velocities and
stresses based on scalar perturbations
can be constructed as
| |
(19) |

Since , velocity fields
based on scalar perturbations are irrotational.
Notice that *Q*^{(0)}= *G*_{0}^{0}, *n*^{i} *Q*_{i}^{(0)}= *G*_{1}^{0} 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.

*Wayne Hu*

*9/9/1997*