On the large-scale instability in interacting dark energy and dark matter fluids

TL;DR

This paper analyzes a dark-sector coupling with $Q = $ $\alpha$ $\mathcal{H}$ $\rho_x$ (positive $\alpha$) between dark energy and dark matter, building on prior work that found large-scale instabilities for other coupling forms. It derives background solutions, examines covariant energy exchange and perturbation equations under two exchange alignments, and studies both super-horizon and sub-horizon behavior. The results show that while an instability persists for nonzero $\alpha$, it can be avoided only if $\alpha$ is very small, implying negligible impact on structure growth prior to dark-energy domination and a late-time decay of dark-matter fluctuations due to conversion from dark energy. Consequently, the coupling offers little observational signature for large-scale structure despite addressing the coincidence problem via a late-time scaling regime. The analysis remains specific to constant-$w$ models; extensions to variable-$w$ scenarios require separate treatment.

Abstract

Recently, Valiviita et al. (2008) have reported a large-scale early-time instability in coupled dark energy and dark matter models. We take the same form of energy-momentum exchange and specialise to the case when the interaction rate is proportional to Hubble's parameter and the dark energy density only. Provided the coupling is made small enough for a given equation of state parameter, we show that the instability can be avoided. Expressions are derived for non-adiabatic modes on super-horizon scales in both the radiation and matter dominated regimes. We also examine the growth of dark matter perturbations in the sub-horizon limit. There we find that the coupling has almost no effect upon the growth of structure before dark energy begins to dominate. Once the universe begins to accelerate, the relative dark matter density fluctuations not only cease to grow as in uncoupled models, but actually decay as the universe continues to expand.

Figures (1)

• Figure 1: The evolution of the dark energy outside the horizon in a matter dominated universe, for modes of three different scales. We take $\alpha = 0.08$ and $w=-0.98$, and $b=1$. The agreement with the analytical approximation is excellent until the mode begins to leave the horizon ($k\tau \sim 1$). Vertical lines indicate when this occurs for each mode.