The effects of anti-correlation on gravitational clustering

Abstract

We use non-linear scaling relations (NSRs) to investigate the effects arising from the existence of negative correlations on the evolution of gravitational clustering in an expanding universe. It turns out that such anti-correlated regions have important dynamical effects on {\it all} scales. In particular, the mere existence of negative values for the linear two-point correlation function $\xib_L$ over some range of scales starting from $l = L_o$, implies that the non-linear correlation function is bounded from above at {\it all} scales $x < L_o$. This also results in the relation $\xib \propto x^{-3}$, at these scales, at late times, independent of the original form of the correlation function. Current observations do not rule out the existence of negative $\xib$ for $ 200 h^{-1}$ Mpc $\la \xib \la 1000 h^{-1}$ Mpc; the present work may thus have relevance for the real Universe. The only assumption made in the analysis is the {\it existence} of the NSR; the results are independent of the form of the NSR as well as of the stable clustering hypothesis.