Interacting dark sector from unimodular gravity: cosmological
  perturbations with no instability
  In unimodular 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. To avoid a gradient
instability, energy must flow from dark matter to dark energy. Finally, we show
that interacting dark energy models with $w=-1$ are equivalent to a class of
generalized dark matter models.
