  In a holographic description of inflation, cosmological time evolution in the
bulk is expected to correspond to the renomalization group (RG) flow in a dual
boundary theory. Here, we analyze this expectation by computing the correlation
functions of the curvature perturbation $\zeta$ holographically. For this
purpose, we use a deformed conformal field theory at the boundary, with a
single deformation operator. In standard single field models of inflation,
$\zeta$ is known to be conserved at large scales under very general conditions.
However, we find that this is not generically the case in the dual description.
The requirement that higher correlators of $\zeta$ should be conserved severely
restricts the possibilities for the RG flow. With such restriction, the power
spectrum $P_\zeta$ must follow an exact power law, at least within the regime
of validity of conformal perturbation theory.
