Dark energy perturbations revisited

In this Letter 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 wD(z)=w0+w1z1+z (for a single fluid or a single scalar field), the dark energy perturbation diverges when its EoS crosses the cosmological constant boundary wD=−1. In this Letter we present a method of treating the dark energy perturbations during the crossing of the wD=−1 surface by imposing matching conditions which require the induced 3-metric on the hypersurface of wD=−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 δD and θD are continuous on the matching hypersurface. This justifies the method used (Zhao et al., 2005, 2007; Xia et al., 2006, 2008) [1], [2], [3], [4] in the numerical calculation and data fitting for the determination of cosmological parameters. We discuss the conditions under which our analysis is applicable.