# Theoretical foundations of the Schrödinger method for LSS formation [CL]

It has been shown that the formation of large scale structures (LSS) in the universe can be described in terms of a Schr$\ddot{o}$dinger-Poisson system. This procedure, known as Schr$\ddot{o}$dinger method, has no theoretical basis, but it is intended as a mere tool to model the N-body dynamics of dark matter halos which form LSS. Furthermore, in this approach the “Planck constant” $\hbar$ in the Schr$\ddot{o}$dinger equation is just a free parameter. In this paper we give a theoretical foundation of the Schr$\ddot{o}$dinger method based on the stochastic quantization introduced by Nelson, and on the Calogero conjecture. The order of magnitude of the effective Planck constant is estimated as $\hbar \sim m^{5/3} G^{1/2} (N/<\rho>)^{1/6}$, where $N$ and $m$ are the number and the mass of the dark matter halos, $<\rho_0>$ is their average density, and $G$ the gravitational constant. The relevance of this finding for the study of LSS is discussed.

F. Briscese
Thu, 15 Dec 16
30/59