Long wavelength limit of evolution of cosmological perturbations in the universe where scalar fields and fluids coexist

TL;DR

This paper derives a long wavelength limit formula for cosmological perturbations involving multiple scalar fields and fluids, providing a tool to analyze early universe phenomena like reheating and curvaton decay.

Contribution

It introduces a general LWL formula that relates cosmological perturbations to homogeneous solutions, including a conserved quantity and correction terms, applicable to complex early universe models.

Findings

Derived the LWL formula for multiple scalar fields and fluids.

Applied the formula to reheating and curvaton models.

Obtained the final amplitude of the Bardeen parameter from initial conditions.

Abstract

We present the LWL formula which represents the long wavelengh limit of the solutions of evolution equations of cosmological perturbations in terms of the exactly homogeneous solutions in the most general case where multiple scalar fields and multiple perfect fluids coexist. We find the conserved quantity which has origin in the adiabatic decaying mode, and by regarding this quantity as the source term we determine the correction term which corrects the discrepancy between the exactly homogeneous perturbations and the $k \to 0$ limit of the evolutions of cosmological perturbations. This LWL formula is useful for investigating the evolutions of cosmological perturbations in the early stage of our universe such as reheating after inflation and the curvaton decay in the curvaton scenario. When we extract the long wavelength limits of evolutions of cosmological perturbations from the exactly homogeneos perturbations by the LWL formula, it is more convenient to describe the corresponding exactly homogeneous system with not the cosmological time but the scale factor as the evolution parameter. By applying the LWL formula to the reheating model and the curvaton model with multiple scalar fields and multiple radiation fluids, we obtain the S formula representing the final amplitude of the Bardeen parameter in terms of the initial adiabatic and isocurvature perturbations Keywords:cosmological perturbations,long wavelength limit,reheating,curvaton PACS number(s):98.80.Cq