... macroscopic

Borrowing the nomenclature from statistical physics.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... analysis

Here it is to be distinguished between the dimensions of comoving and physical lengths, differing by a factor a(t).

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... densities

The data tend to follow the fit also for very small densities as long as mass-resolution effects are not large.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... fields

In the mathematical manipulations in this Appendix, one can assume that the Dirac delta is regularized by a short-distance cutoff which is set to zero in the final results. In this way, the field  ${\vec u}_{\rm mic} ({\vec x})$ is defined, and not only the product  $\varrho_{\rm mic} {\vec u}_{\rm mic} ({\vec x})$.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.