$\delta N$ formalism from superpotential and holography

TL;DR

This paper extends the superpotential formalism to non-canonical inflation models, linking it with holography, and demonstrates its utility in analyzing primordial perturbations and attractor behavior.

Contribution

It generalizes the superpotential approach to include non-canonical kinetic terms and connects inflationary dynamics with holographic duality, providing new tools for perturbation analysis.

Findings

Superpotential formalism is applicable to non-canonical inflation models.

The approach justifies the separate universe approximation.

Computed primordial spectra match conformal perturbation theory results.

Abstract

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.