Late universe dynamics with scale-independent linear couplings in the dark sector

TL;DR

The paper examines a late-time cosmology with two coupled dark components using a scale-independent interaction Q = \frac{3}{2} H q(\rho_A,\rho_B) and a linear expansion q(\rho_A,\rho_B) = q_0 + q_A \rho_A + q_B \rho_B. It develops a dynamical-systems framework, deriving autonomous equations for ρ_T and Δ and identifying fixed points that realize an effective cosmological constant, including cases with affine-like evolution. It further classifies three representative couplings (I–III) and analyzes the evolution of density parameters, showing that Λ-like behavior can emerge from either q_0 or the fixed-point structure (w_eff = -1). Using SN Ia data (192 SNe) with w_B = 0, the authors find Ω_Λ unconstrained, best-fit Ω_{0A} around 0.63–0.76, and a preference for couplings proportional to the DE density, especially under strong coupling with phantom DE (w_A < -1) favoring positive q_A. The work highlights that coupled dark-energy models can mimic ΛCDM at the background level and underscores the need for complementary data (CMB, LSS) and perturbation analyses to tighten constraints and assess viability.

Abstract

We explore the dynamics of cosmological models with two coupled dark components with energy densities $ρ_A$ and $ρ_B$. We assume that the coupling is of the form $Q=Hq(ρ_A,ρ_B)$, so that the dynamics of the two components turns out to be scale independent, i.e. does not depend explicitly on the Hubble scalar $H$. With this assumption, we focus on the general linear coupling $q=q_o+q_Aρ_A+q_Bρ_B$, which may be seen as arising from any $q(ρ_A,ρ_B)$ at late time and leads in general to an effective cosmological constant. In the second part of the paper we consider observational constraints on the form of the coupling from SN Ia data, assuming that one of the components is cold dark matter. We find that the constant part of the coupling function is unconstrained by SN Ia data and, among typical linear coupling functions, the one proportional to the dark energy density $ρ_{A}$ is preferred in the strong coupling regime, $|q_{A}|>1$. While phantom models favor a positive coupling function, in non-phantom models, not only a negative coupling function is allowed, but the uncoupled sub-case falls at the border of the likelihood.

Figures (5)

• Figure 1: Upper panel: evolutions of the energy density parameters $\Omega_{A}$ (thin solid line), $\Omega_{B}$ (dotted line) and $\Omega_{\gamma}$ (thick solid line) for a model with $q_{+}=q_{-}=0.25$; for comparison, the dashed lines are the values of $x$ and $y$ at the fixed points B (thin short-dashed lines) and C (thick long-dashed lines). For this model the parameters are: $\Omega_{0A}=\Omega_{\Lambda}=0.5$, $w_{A}=0$, $w_{B}=-1.5$, $\beta_{+}=0$ and $\beta_{-}=-1.25$. Lower panel: the total effective EoS parameter for the same model : $w_{eff}$ evolves from the value $1/3$ in the radiation dominated era, approaches the value $~0$ in the matter dominated era and then asymptotically evolves toward a constant phantom value, in this case $\beta_{-}=-1.25$.
• Figure 2: Upper panel: evolutions for the energy density parameters for a model with $q_{-}=0$ and $q_{+}=-0.5$; for comparison, the dashed lines are the values of $x$ and $y$ at the fixed points B (thin short-dashed lines) and D (thick long-dashed lines). For this model the parameters are: $\Omega_{0A}=\Omega_{\Lambda}=0.5$, $w_{A}=-1.1$, $w_{B}=0.2$. Lower panel: effective EoS for the same model; for comparison, we plot the EoS parameter of the fixed point B, $\beta_{+}=-0.14$.
• Figure 3: Upper panel: evolutions for the energy density parameters for a model with $q_{+}=0$ and $q_{-}=-0.18$; for comparison, the dashed lines are the values of $x$ and $y$ at the fixed point B (thin short-dashed lines) and D (thick long-dashed lines). For this model the parameters are: $\Omega_{0A}=0.5$, $\Omega_{\Lambda}=0$, $w_{A}=-0.9$, $w_{B}=0.$ (dust). The EoS parameters at B are $\beta_{+}=-0.08$ and $\beta_{-}=-1$. Lower panel: effective EoS for the same model.
• Figure 4: Coupling diagrams with two-dimensional likelihood for models with $\Omega_{\Lambda}=0$. Apart from the short-dashed line that represents an affine evolution with $\beta_{+/-}=-1$, all the other lines are labeled with the corresponding type of coupling function (e.g. the solid line on the left side diagrams represents a coupling function $Q\propto\rho_{B}$ (model I), while on the right side diagrams it represents $Q\propto \rho_{T}$ (model II)). The energy density parameter at present is fixed at its best fit value, respectively $\Omega_{0A}=0.63, 0.65, 0.76$.
• Figure 5: Coupling diagrams with two-dimensional likelihood for models with $\Omega_{\Lambda}=0.7$. All the lines are labeled with the corresponding type of coupling function (e.g. the solid line on the left side diagrams represents a coupling function $Q\propto\rho_{B}$ (model I), while on the right side diagrams it represents $Q\propto \rho_{T}$ (model II)). The short-dashed line represents affine evolution with $\beta_{+/-}=-1$ and the short-dashed curve represents affine evolution with $\beta_{+}=\beta_{-}$ . The energy density parameter at present is fixed at its best fit value, respectively $\Omega_{0A}=0.63, 0.65, 0.76$.