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