Cosmological Instabilities and the Role of Matter Interactions in
  Dynamical Dark Energy Models
  We consider cosmological models with a dynamical dark energy field, and study
the presence of three types of commonly found instabilities, namely ghost (when
fields have negative kinetic energy), gradient (negative momentum squared) and
tachyon (negative mass squared). In particular, we study the linear scalar
perturbations of theories with two interacting scalar fields as a proxy for a
dark energy and matter fields, and explicitly show how canonical
transformations relate these three types of instabilities with each other. We
generically show that low-energy ghosts are equivalent to tachyonic
instabilities, and that high-energy ghosts are equivalent to gradient
instabilities. Via examples we make evident the fact that whenever one of these
fields exhibits an instability then the entire physical system becomes
unstable, with an unbounded Hamiltonian. Finally, we discuss the role of
interactions between the two fields, and show that whereas most of the time
interactions will not determine whether an instability is present or not, they
may affect the timescale of the instability. We also find exceptional cases in
which the two fields are ghosts and hence the physical system is seemingly
unstable, but the presence of interactions actually lead to stable solutions.
These results are very important for assessing the viability of dark energy
models that may exhibit ghost, gradient or tachyonic modes.
