Stable Clustering Ansatz, Consistency Relations and Gravity Dual of Large-Scale Structure

Abstract: Gravitational clustering in the nonlinear regime remains poorly understood. Gravity dual of gravitational clustering has recently been proposed as a means to study the nonlinear regime. The stable clustering ansatz remains a key ingredient to our understanding of gravitational clustering in the highly nonlinear regime. We study certain aspects of violation of the stable clustering ansatz in the gravity dual of Large Scale Structure (LSS). We extend the recent studies of gravitational clustering using AdS gravity dual to take into account possible departure from the stable clustering ansatz and to arbitrary dimensions. Next, we extend the recently introduced consistency relations to arbitrary dimensions. We use the consistency relations to test the commonly used models of gravitational clustering including the halo models and hierarchical ans\"atze. In particular we establish a tower of consistency relations for the hierarchical amplitudes: $Q, R_a, R_b, S_a,S_b,S_c$ etc. as a functions of the scaled peculiar velocity $h$. We also study the variants of popular halo models in this context. In contrast to recent claims, none of these models, in their simplest incarnation, seem to satisfy the consistency relations in the soft limit.