# Non-Gaussianity of superhorizon curvature perturbations beyond $δ$ N formalism - Astrophysics > Cosmology and Nongalactic Astrophysics

Non-Gaussianity of superhorizon curvature perturbations beyond $δ$ N formalism - Astrophysics > Cosmology and Nongalactic Astrophysics - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: We develop a theory of nonlinear cosmological perturbations on superhorizonscales for a single scalar field with a general kinetic term and a general formof the potential. We employ the ADM formalism and the spatial gradientexpansion approach, characterised by $O\epsilon^m$, where $\epsilon=1-HL$is a small parameter representing the ratio of the Hubble radius to thecharacteristic length scale $L$ of perturbations. We obtain the generalsolution for a full nonlinear version of the curvature perturbation valid upthrough second-order in $\epsilon$ $m=2$. We find the solution satisfies anonlinear second-order differential equation as an extension of the equationfor the linear curvature perturbation on the comoving hypersurface. Then weformulate a general method to match a perturbative solution accurate to$n$-th-order in perturbation inside the horizon to our nonlinear solutionaccurate to second-order $m=2$ in the gradient expansion on scales slightlygreater than the Hubble radius. The formalism developed in this paper allows usto calculate the superhorizon evolution of a primordial non-Gaussianity beyondthe so-called $\delta N$ formalism or separate universe approach which isequivalent to leading order $m=0$ in the gradient expansion. In particular,it can deal with the case when there is a temporary violation of slow-rollconditions. As an application of our formalism, we consider Starobinsky-smodel, which is a single field model having a temporary non-slow-roll stage dueto a sharp change in the potential slope. We find that a large non-Gaussianitycan be generated even on superhorizon scales due to this temporary suspensionof slow-roll inflation.

Autor: Yu-ichi Takamizu, Shinji Mukohyama, Misao Sasaki, Yoshiharu Tanaka

Fuente: https://arxiv.org/