Long wavelength limit of evolution of nonlinear cosmological perturbations

TL;DR

This paper develops a comprehensive nonlinear perturbation theory for cosmological models with multiple scalar fields and fluids, deriving gauge-invariant variables and formulas for long wavelength evolution, and analyzes the suppression of nonlinear parameters during slow roll.

Contribution

It introduces a new long wavelength limit formula and gauge-invariant variables for nonlinear cosmological perturbations with multiple fields and fluids, extending previous linear approaches.

Findings

Derived constraints from the momentum condition for locally homogeneous universes.

Constructed gauge-invariant perturbation variables at arbitrary nonlinear order.

Showed nonlinear parameters like fNL and gNL are suppressed by slow roll parameters.

Abstract

In the general matter composition where the multiple scalar fields and the multiple perfect fluids coexist, in the leading order of the gradient expansion, we construct all of the solutions of the nonlinear evolutions of the locally homogeneous universe. From the momentum constraint, we derive the constraints which the solution constants of the locally homogeneous universe must satisfy. We construct the gauge invariant perturbation variables in the arbitrarily higher order nonlinear cosmological perturbation theory around the spatially flat Friedmann-Robertson-Walker universe. We construct the nonlinear long wavelength limit formula representing the long wavelength limit of the evolution of the nonlinear gauge invariant perturbation variables in terms of perturbations of the evolutions of the locally homogeneous universe. By using the long wavelength limit formula, we investigate the evolution of nonlinear cosmological perturbations in the universe dominated by the multiple slow rolling scalar fields with an arbitrary potential. The tau function and the N potential introduced in this paper make it possible to write the evolution of the multiple slow rolling scalar fields with an arbitrary interaction potential and the arbitrarily higher order nonlinear Bardeen parameter at the end of the slow rolling phase analytically. It is shown that the nonlinear parameters such as fNL and gNL are suppressed by the slow rolling expansion parameters.