Interacting dark sector from the trace-free Einstein equations: cosmological perturbations with no instability

Understand

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 $w=-1$.

• 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 $w_{\rm eff}\neq0$ 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.