Consistency relations and conservation of $\zeta$ in holographic
  inflation
  It is well known that, in single clock inflation, the curvature perturbation
$\zeta$ is constant in time on superhorizon scales. In the standard bulk
description this follows quite simply from the local conservation of the energy
momentum tensor in the bulk. On the other hand, in a holographic description,
the constancy of the curvature perturbation must be related to the properties
of the RG flow in the boundary theory. Here, we show that, in single clock
holographic inflation, the time independence of correlators of $\zeta$ follows
from the cut-off independence of correlators of the energy momentum tensor in
the boundary theory, and from the so-called consistency relations for vertex
functions with a soft leg.
