$\delta N$ formalism from superpotential and holography

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.

37 pages

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• A simple, exact, model of quasi-single field inflation
• Holography for the very early Universe and the classic puzzles of Hot Big Bang cosmology
• Universality in generalized models of inflation
• Regularized-Renormalized-Resummed loop corrected power spectrum of non-singular bounce with Primordial Black Hole formation
• Anisotropic separate universe and Weinberg's adiabatic mode
• Hubble multi-scalar inflation
• An Hamilton-Jacobi formulation of anisotropic inflation
• Primordial Black Holes from Effective Field Theory of Stochastic Single Field Inflation at NNNLO
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• Negative non-Gaussianity as a salvager for PBHs with PTAs in bounce
• Holographic cosmology solutions of problems with pre-inflationary cosmology
• $\Delta N$ Formalism and Conserved Currents in Cosmology
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