Interacting dark sector from the trace-free Einstein equations: Cosmological perturbations with no instability
Marco de Cesare, Edward Wilson-Ewing
Abstract
In trace-free Einstein gravity, the stress-energy tensor of matter is not necessarily conserved and so the theory offers a natural framework for interacting dark energy models where dark energy has a constant equation of state $w=\ensuremath{-}1$. We derive the equations of motion for linear cosmological perturbations in interacting dark energy models of this class, focusing on the scalar sector. Then, we consider a specific model where the energy-momentum transfer potential is proportional to the energy density of cold dark matter; this transfer potential has the effect of inducing an effective equation of state ${w}_{\mathrm{eff}}\ensuremath{\ne}0$ for cold dark matter. We analyze in detail the evolution of perturbations during radiation domination on super-Hubble scales, finding that the well-known large-scale instability that affects a large class of interacting dark energy models is absent in this model. To avoid a gradient instability, energy must flow from dark matter to dark energy. Finally, we show that interacting dark energy models with $w=\ensuremath{-}1$ are equivalent to a class of generalized dark matter models.