$\delta N$ formalism from superpotential and holography
  We consider the superpotential formalism to describe the evolution of scalar
fields during inflation, generalizing it to include the case with non-canonical
kinetic terms. We provide a characterization of the attractor behaviour of the
background evolution in terms of first and second slow-roll parameters (which
need not be small). We find that the superpotential is useful in justifying the
separate universe approximation from the gradient expansion, and also in
computing the spectra of primordial perturbations around attractor solutions in
the $\delta N$ formalism. As an application, we consider a class of models
where the background trajectories for the inflaton fields are derived from a
product separable superpotential. In the perspective of the holographic
inflation scenario, such models are dual to a deformed CFT boundary theory,
with $D$ mutually uncorrelated deformation operators. We compute the bulk power
spectra of primordial adiabatic and entropy cosmological perturbations, and
show that the results agree with the ones obtained by using conformal
perturbation theory in the dual picture.
