Dark degeneracy I: Dynamical or interacting dark energy?
  We revisit the dark degeneracy that arises from the Einstein equations
relating geometry to the total cosmic substratum but not resolving its
individual components separately. We establish the explicit conditions for the
dark degeneracy in the fluid description of the dark sector. At the background
level, this degeneracy can be formally understood in terms of a unified dark
sector Equation of State (EoS) that depends both on the dynamical nature of the
dark energy (DE) as well as on its interaction with the pressureless dark
matter. For linear perturbations, the degeneracy arises for specified DE
pressure perturbations (or sound speed, equivalently) and DE anisotropic
stress. Specializing to the degeneracy between non-interacting dynamical DE and
interacting vacuum DE models, we perform a parameter estimation analysis for a
range of dynamical DE parametrizations, where for illustration we explicitly
break the degeneracy at the linear level by adopting a luminal sound speed for
both scenarios. We conduct this analysis using cosmological background data
alone and in combination with Planck measurements of the cosmic microwave
background radiation. We find that although the overall phenomenology between
the dynamical DE and interacting approaches is similar, there are some
intriguing differences. In particular, there is an ambiguity in the strength of
constraints on $\Omega_{m0}$ and $\sigma_8$, which are considerably weakened
for interacting vacuum DE, indicating that the dark degeneracy can change the
significance of tensions in cosmological parameters inferred from different
data sets.
