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Application of the beyond δN formalism: Varying sound speed

Yu-ichi Takamizu*

  • Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan and Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom

  • *takamizu@yukawa.kyoto-u.ac.jp; yt313@cam.ac.uk

Phys. Rev. D 89, 043528 – Published 28 February, 2014

DOI: https://doi.org/10.1103/PhysRevD.89.043528

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 δN 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 δN formalism, where curvature perturbations remain just constant, and nonlinear curvature perturbation follows the simple master equation whose form is similar to 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.

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