$\delta$N formalism from superpotential and holography

Jaume Garriga (1, 2) , Yuko Urakawa (3, 4) , Filippo Vernizzi (5, 6)

1 UB - Universitat de Barcelona
2 Tufts University [Medford]
3 Nagoya University
4 IAS - Institute for Advanced Study [Princeton]
5 IPHT - Institut de Physique Théorique - UMR CNRS 3681
6 Physics Department [Genève]

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.

Mots clés: inflation; cosmological perturbation theory

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Relativité Générale et Cosmologie Quantique [gr-qc]

Jaume Garriga, Yuko Urakawa, Filippo Vernizzi. $\delta$N formalism from superpotential and holography. Journal of Cosmology and Astroparticle Physics, 2016, 2016, pp.036. ⟨10.1088/1475-7516/2016/02/036⟩. ⟨cea-01223811⟩