Cosmological long-wavelength solutions in non-adiabatic multi-fluid systems

TL;DR

This paper formulates nonlinear superhorizon cosmological perturbations in multi-fluid systems, capturing both adiabatic and entropy modes at nonlinear order using a gradient expansion approach.

Contribution

It introduces a new nonlinear framework for multi-fluid cosmological perturbations on superhorizon scales, including explicit solutions and mode analysis.

Findings

Constructed explicit nonlinear long-wavelength solutions for multi-fluid perturbations.

Identified the presence of both adiabatic and entropy modes at leading nonlinear order.

Analyzed the evolution of curvature and density perturbations under different initial conditions.

Abstract

We develop a formulation of nonlinear cosmological perturbations on superhorizon scales in multi-fluid systems. It is based on the Arnowitt-Deser-Misner formalism combined with a spatial gradient expansion characterized by a small expansion parameter defined as the ratio of the comoving wavenumber to the Hubble scale. The background spacetime is assumed to be a flat Friedmann-Lemaitre-Robertson-Walker universe. Within this framework, we explicitly construct nonlinear long-wavelength solutions for cosmological perturbations. Since multi-fluid systems are inherently non-adiabatic, these solutions admit both adiabatic and entropy modes already at leading nonlinear order. We define adiabatic and entropy perturbations and discuss the non-uniqueness in defining pure entropy perturbations. Using different choices of pure entropy initial conditions, we analyze the time evolution of physical quantities such as the curvature perturbation and density perturbations in the geodesic slicing for two-fluid systems.