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We study non-linear gravitational clustering from cold gaussian power-lawinitial conditions in a family of scale-free EdS models, characterized by afree parameter $\kappa$ fixing the ratio between the mass driving the expansionand the mass which clusters. As in the "usual" EdS model, corresponding to$\kappa=1$, self-similarity provides a powerful instrument to delimit thephysically relevant clustering resolved by a simulation. Likewise, if stableclustering applies, it implies scale-free non-linear clustering. We derive thecorresponding exponent $\gamma_{sc} (n, \kappa)$ of the two point correlationfunction. We then report the results of extensive N-body simulations, ofcomparable size to those previously reported in the literature for the case$\kappa=1$, and performed with an appropriate modification of the GADGET2 code.We observe in all cases self-similarity in the two point correlations, down toa lower cut-off which decreases monotonically in time in comoving coordinates.The self-similar part of the non-linear correlation function is fitted well inall cases by a single power-law with an exponent in good agreement with$\gamma_{sc} (n, \kappa)$. Our results thus indicate that stable clusteringprovides an excellent approximation to the non-linear correlation function overthe resolved self-similar scales, at least down to $\gamma_{sc} (n, \kappa)\approx 1$, corresponding to the case $n=-2$ for $\kappa=1$. We conclude, incontrast notably with the results of Smith et al. (2003), that a clearidentification of the breakdown of stable clustering in self-similar models -and the possible existence of a "universal" region in which non-linearclustering becomes independent of initial conditions - remains an importantopen problem, which should be addressed further in significantly largersimulations.

Self-similarity and stable clustering in a family of scale-free cosmologies