Application of beyond $\delta N$ formalism -- Varying sound speed

Abstract

We focus on the evolution of curvature perturbation on superhorizon scales by adopting the spatial gradient expansion and show that the nonlinear theory, called the beyond $\delta N$-formalism as the next-leading order in the expansion. As one application of our formalism for a single scalar field, we investigate the case of varying sound speed. In our formalism, we can deal with the time evolution in contrast to $\delta N$-formalism, where curvature perturbations remain just constant, and nonlinear curvature perturbation follows the simple master equation whose form is similar as one in linear theory. So the calculation of bispectrum can be done in the next-leading order in the expansion as similar as the case of deriving the power spectrum. We discuss localized features of both primordial power and bispectrum generated by the effect of varying sound speed with a finite duration time. We can see a local feature like a bump in the equilateral bispectrum.

8 pages, 6 figures. References added

References in corpus (8)

• The Effective Field Theory of Inflation Models with Sharp Features
• Gradient expansion approach to nonlinear superhorizon perturbations
• The effect of varying sound velocity on primordial curvature perturbations
• Non-Gaussianity of superhorizon curvature perturbations beyond $\delta$ N formalism
• Gradient expansion approach to nonlinear superhorizon perturbations II -- a single scalar field --
• Local non-Gaussianity from rapidly varying sound speeds
• Nonlinear superhorizon perturbations of non-canonical scalar field
• Full nonlinear growing and decaying modes of superhorizon curvature perturbations

Cited by in corpus (2)

• Untangling features in the primordial spectra
• Consistency conditions and primordial black holes in single field inflation