Dark Energy Perturbations Revisited

TL;DR

This paper revisits the evolution of dark energy perturbations, proposing a matching method to handle divergences at the w_D=-1 boundary, ensuring continuity and consistency in cosmological models.

Contribution

It introduces a matching condition approach to treat dark energy perturbations during the crossing of w_D=-1, improving the robustness of cosmological perturbation analysis.

Findings

Dark energy perturbations are continuous across w_D=-1 crossing.

The matching conditions justify previous numerical methods.

The approach applies to various early universe models.

Abstract

In this paper we study the evolution of cosmological perturbations in the presence of dynamical dark energy, and revisit the issue of dark energy perturbations. For a generally parameterized equation of state (EoS) such as w_D(z) = w_0+w_1\frac{z}{1+z}, (for a single fluid or a single scalar field ) the dark energy perturbation diverges when its EoS crosses the cosmological constant boundary w_D=-1. In this paper we present a method of treating the dark energy perturbations during the crossing of the $w_D=-1$ surface by imposing matching conditions which require the induced 3-metric on the hypersurface of w_D=-1 and its extrinsic curvature to be continuous. These matching conditions have been used widely in the literature to study perturbations in various models of early universe physics, such as Inflation, the Pre-Big-Bang and Ekpyrotic scenarios, and bouncing cosmologies. In all of these cases the EoS undergoes a sudden change. Through a detailed analysis of the matching conditions, we show that \delta_D and \theta_D are continuous on the matching hypersurface. This justifies the method used[1-4] in the numerical calculation and data fitting for the determination of cosmological parameters. We discuss the conditions under which our analysis is applicable.