The growth of angular momentum in a general clustering scenario is analyzed and its correlation with the primordial density perturbation delta₀ is calculated. High-density peaks are found to evolve into low-angular momentum systems. The basic mechanism behind this anticorrelation is that anisotropic structure, which leads to angular momentum gain, is statistically uncorrelated with the primordial perturbation. The collapse time, on the other hand, is correlated with it. This time scale is the one that determines the angular momentum of a bound object. Three cases are studied, and the correlation of J with delta₀ is calculated: (1) Lagrangian sphere (quasi-linear evolution); (2) Eulerian sphere (second order in delta); (3) arbitrary Lagrangian volume (first order in delta).
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Yehuda Hoffman (1986) studied this question.