3.2. Topology

An analysis of the present day topology of the large-scale structure in the universe (Weinberg, Gott and Melott 1987) is directly related to the topology of the initial density fluctuations. The series of papers by Gott and his collaborators detail the way a measure of the topology - the genus of contours of a smoothed density distribution of galaxies - can be studied to determine the type of initial density fluctuations that existed in the early epochs of the universe.

The available data is sparse, and the relation between the genus and the threshold density has to be made from this available sample. The process involved in obtaining this relation involves smoothing the data, drawing the contour and then determining the genus per unit volume.

Figure 7, taken from Weinberg, Gott and Melott (1987) shows the contours for the CfA data (Huchra et al. 1983), drawn at various thresholds, v, of volume fractions, containing respectively 7%, 16%, 24% and 50% of the low dshow the mean values obtained for the bootstrap models. As mentioned the bootstrap is a procedure for determining the variance and not the mean values. No significance should be attached to the position of the squares.

Figure 7.

Figure 8.