Dark coupling

TL;DR

This work formalizes a general dark sector coupling between dark matter and dark energy, identifies a doom factor that governs non-adiabatic instabilities in linear perturbations, and establishes stability conditions. It analyzes a simple viable model with Q ∝ ρ_de, showing that negative coupling (ξ<0) yields a stable and observationally allowed cosmology, with distinctive effects on background evolution, perturbations, and degeneracies with neutrino mass and curvature. The paper also compares to models with Q ∝ ρ_dm, which tend to exhibit early-time instabilities, and discusses how dynamical w or time-dependent couplings may mitigate these issues. Overall, sizable dark coupling values are compatible with current data and have measurable implications for structure formation and reconstructed equations of state.

Abstract

The two dark sectors of the universe - dark matter and dark energy - may interact with each other. Background and linear density perturbation evolution equations are developed for a generic coupling. We then establish the general conditions necessary to obtain models free from early time non-adiabatic instabilities. As an application, we consider a viable universe in which the interaction strength is proportional to the dark energy density. The scenario does not exhibit "phantom crossing" and is free from instabilities, including early ones. A sizeable interaction strength is compatible with combined WMAP, HST, SN, LSS and H(z) data. Neutrino mass and/or cosmic curvature are allowed to be larger than in non-interacting models. Our analysis sheds light as well on unstable scenarios previously proposed.

Figures (10)

• Figure 1: Left panel: The blue (red) curve depicts the evolution of the $\delta_{dm}$ perturbation vs the scale factor for $k=0.001$ h/Mpc and $w=-1.1$ ($w=-0.9$). Right panel: same as in the left panel but for the $\delta_{de}$ evolution.
• Figure 2: Scenario with $Q \propto \rho_{de}$. Relative energy densities of dark matter plus baryons $\Omega_{dm+b}$ (blue), radiation $\Omega_{rad}$ (black) and dark energy $\Omega_{de}$ (red), as a function of the scale factor $a$, for w=-0.9. Three values of the coupling are illustrated: $\xi= 0$ (solid curve), $0.25$ (long dashed curve) and $-0.25$ (short dashed curve).
• Figure 3: Scenario with $Q\propto \mathcal{\rho}_{de}$. Reconstructed $\tilde{w}(z)$ as function of $z$, for $w= -0.9$. The black (solid) and magenta (short dashed) curves depict the $\tilde{w}(z)$ behaviour for $\xi=0.2$ and $\xi= 0.8$. The blue (long-short dashed) and the red (long dashed) curves denote the $\tilde{w}(z)$ behaviour for $\xi=-0.2$ and $\xi=-0.8$. Notice that for positive values of $\xi$ we recover the divergent phantom-crossing behavior appearing in scalar-tensor theories.
• Figure 4: Scenario with $Q\propto \rho_{de}$ in the strong coupling regime. Left (right) panel: Evolution of the $\delta_{de}$ perturbation vs the scale factor for scales $k=0.001$ h/Mpc, for $\xi=-0.8$ and $w=-0.9$ ($w=-1.1$). Notice the early time instability present when the doom factor ${\bf d }$ in Eq. (\ref{['eq:maldito_us']}) is sizeable and positive, as predicted from the study of the instabilities.
• Figure 5: Scenario with $Q\propto \rho_{de}$. Left (right) panel: 1$\sigma$ and 2$\sigma$ marginalized contours in the $\xi$--$\Omega_{dm} h^2$ ($\xi$--$\Omega_k$) plane. The largest, green contours show the current constraints from WMAP (5 year data), HST, SN and $H(z)$ data. The smallest, red contours show the current constraints from WMAP (5 year data), HST, SN, $H(z)$ and LSS data.