Large-scale stable interacting dark energy model: Cosmological perturbations and observational constraints

Dark energy might interact with cold dark matter in a direct, nongravitational way. However, the usual interacting dark energy models (with constant w) suffer from some catastrophic difficulties. For example, the Q proportional to rho(c) model leads to an early-time large-scale instability, and the Q proportional to rho(de) model gives rise to the future unphysical result for cold dark matter density (in the case of a positive coupling). In order to overcome these fatal flaws, we propose in this paper an interacting dark energy model (with constant w) in which the interaction term is carefully designed to realize that Q proportional to rho(de) at the early times and Q proportional to rho(c) in the future, simultaneously solving the early-time superhorizon instability and future unphysical rho(c) problems. The concrete form of the interaction term in this model is Q = 3 beta H rho(de)rho(c)/rho(de)+rho(c), where beta is the dimensionless coupling constant. We show that this model is actually equivalent to the decomposed new generalized Chaplygin gas (NGCG) model, with the relation beta = -aw. We calculate the cosmological perturbations in this model in a gauge-invariant way and show that the cosmological perturbations are stable during the whole expansion history provided that beta > 0. Furthermore, we use the Planck data in conjunction with other astrophysical data to place stringent constraints on this model (with eight parameters), and we find that indeed beta > 0 is supported by the joint constraint at more than 1 sigma level. The excellent theoretical features and the support from observations all indicate that the decomposed NGCG model deserves more attention and further investigation.