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

Understand

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.