Interacting Dark Energy and Cosmological Equations of State

TL;DR

The paper investigates how interactions in the dark sector between DM and DE modify background expansion and perturbation dynamics. It adopts a two-component fluid with decay rate $\Gamma$ and derives the background equations $H^2=\frac{8\pi G}{3}\rho$ and $\dot H=-4\pi G(\rho+p_X)$ along with $\dot{\rho}_M+3H\rho_M=\Gamma\rho_X$, $\dot{\rho}_X+3H(1+w_X)\rho_X=-\Gamma\rho_X$, and shows that a stationary ratio $\kappa_0$ yields $w=\frac{w_X}{1+\kappa_0}$ and $\Gamma = -3H\frac{\kappa_0}{1+\kappa_0}w_X$, giving $\rho_M,\rho_X\propto a^{-3(1+w)}$. The work also notes that any one-component EOS can be recast as an interacting two-component model, highlighting degeneracies and guiding perturbation analysis. It further demonstrates that fluctuations in $\Gamma$ induce non-adiabatic perturbations characterized by an effective sound speed $c_{\rm eff}^2 = \frac{\dot p}{\dot\rho}+\lambda$ and a time-dependent curvature perturbation $\zeta$, which modulates the ISW effect and can yield a smaller ISW signal than in $\Lambda$CDM. These results have implications for addressing the coincidence problem, holographic DE, and the avoidance of a big rip, while offering testable predictions for luminosity-distance measurements and CMB anisotropies.

Abstract

Interactions within the cosmic medium modify its equation of state. We discuss implications of interacting dark energy models both for the spatially homogenous background and for the perturbation dynamics.