Interacting Dark Energy: Summary of models, Pathologies, and Constraint

Abstract

We present an overview of the main results from our two companion papers that are relevant for observational constraints on interacting dark energy (IDE) models. We provide analytical solutions for the dark matter and dark energy densities, 𝜌dm and 𝜌de, as well as the normalized Hubble function ℎ(𝑧), for eight IDE models. These include five linear IDE models, namely 𝑄 = 3𝐻(𝛿dm𝜌dm +𝛿de𝜌de) and four special cases: 𝑄 = 3𝐻𝛿(𝜌dm +𝜌de), 𝑄 = 3𝐻𝛿(𝜌dm − 𝜌de), 𝑄 = 3𝐻𝛿𝜌dm, and 𝑄 = 3𝐻𝛿𝜌de, together with three non-linear IDE models: 𝑄 = 3𝐻𝛿 ( 𝜌dm𝜌de 𝜌dm+𝜌de ),𝑄 = 3𝐻𝛿 (𝜌2dm𝜌dm+𝜌de ), and 𝑄 = 3𝐻𝛿 (𝜌2de𝜌dm+𝜌de ) . For these eight models, we present conditions to avoid imaginary, undefined, and negative energy densities. In seven of the eight cases, negative densities arise if energy flows from DM to DE, implying a strong theoretical preference for energy transfer from DE to DM. We also provide conditions to avoid future big rip singularities and evaluate how each model addresses the coincidence problem in both the past and the future. Finally, we propose a set of approaches and simplifying assumptions that can be used when constraining IDE models, by defining regimes that restrict the parameter space according to the behavior researchers are willing to tolerate