GRAVITATIONAL-FIELD FLUCTUATIONS IN WEAKLY CLUSTERED SYSTEMS

Stochastic fluctuations of the gravitational field in a collisionless, weakly clustered protogalactic system are induced by local fluctuations in the number density of small collapsed peaks. We calculate the probability distribution of the stochastic forces generated by these fluctuations, and we find a generalization of the Holtsmark distribution, previously studied in a stellar dynamical context by Chandrasekhar and Von Neumann and by Kandrup. We also find the probability distribution of the torques induced by these stochastic forces, introducing the analog of the Holtsmark law for the torque distribution, and we study different cases corresponding to different power laws. We apply these considerations to realistic models of protogalactic and protocluster density perturbations. The force probability distribution is remarkably influenced by the clustering of substructure: the profile is more strongly peaked, and the asymptotic decay W(F) --> F-5/2 is almost suppressed, resulting in an enhanced probability near the average value. The consequences of this fact on the calculation of the dynamical evolution of cosmological density perturbations, which will be developed in a subsequent paper, are stressed.