Long wavelength limit of evolution of nonlinear cosmological perturbations

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.

References in corpus (4)

• Curvature and isocurvature perturbations from two-field inflation in a slow-roll expansion
• Gauge-invariant Formulation of the Second-order Cosmological Perturbations
• Gradient expansion approach to nonlinear superhorizon perturbations
• Long wavelength limit of evolution of cosmological perturbations in the universe where scalar fields and fluids coexist

Cited by in corpus (11)

• δN formalism
• Stochastic inflation at all order in slow-roll parameters: foundations
• Gravitational Wave Background and Non-Gaussianity as a Probe of the Curvaton Scenario
• Non-Gaussianity of superhorizon curvature perturbations beyond $\delta$ N formalism
• Reheating, Multifield Inflation and the Fate of the Primordial Observables
• Local Features with Large Spiky non-Gaussianities during Inflation
• \bf $\delta M$ Formalism: A New Approach to Cosmological Perturbation Theory in Anisotropic Inflation
• Gravitino Dark Matter and Non-Gaussianity
• Fully non-linear equivalence of delta N and covariant formalisms
• Manifestly gauge invariant theory of the nonlinear cosmological perturbations in the leading order of the gradient expansion
• Construction and applications of the manifestly gauge invariant expressions of the solutions of the cosmological perturbation theory