Cosmological perturbations in models of coupled dark energy

Models in which dark energy interacts with dark matter have been proposed in the literature to help explain why dark energy should only come to dominate in recent times. In this paper, we present a dynamical framework to calculate cosmological perturbations for a general quintessence potential and interaction term. Our formalism is built upon the powerful phase-space approach often used to analyze the dynamical attractors in the background. We obtain a set of coupled differential equations purely in terms of dimensionless, bounded variables and apply these equations to calculate perturbations in a number of scenarios. Interestingly, in the presence of dark-sector interactions, we find that dark energy perturbations do not redshift away at late times, but can cluster even on small scales. We also clarify the initial conditions for the perturbations in the dark sector, showing that adiabaticity is no longer conserved in the presence of dark-sector interactions, even on large scales. Some issues of instability in the perturbations are also discussed.