Constraining early and interacting dark energy with gravitational wave
  standard sirens: the potential of the eLISA mission
  We perform a forecast analysis of the capability of the eLISA space-based
interferometer to constrain models of early and interacting dark energy using
gravitational wave standard sirens. We employ simulated catalogues of standard
sirens given by merging massive black hole binaries visible by eLISA, with an
electromagnetic counterpart detectable by future telescopes. We consider
three-arms mission designs with arm length of 1, 2 and 5 million km, 5 years of
mission duration and the best-level low frequency noise as recently tested by
the LISA Pathfinder. Standard sirens with eLISA give access to an intermediate
range of redshift $1\lesssim z \lesssim 8$, and can therefore provide
competitive constraints on models where the onset of the deviation from
$\Lambda$CDM (i.e. the epoch when early dark energy starts to be
non-negligible, or when the interaction with dark matter begins) occurs
relatively late, at $z\lesssim 6$. If instead early or interacting dark energy
is relevant already in the pre-recombination era, current cosmological probes
(especially the cosmic microwave background) are more efficient than eLISA in
constraining these models, except possibly in the interacting dark energy model
if the energy exchange is proportional to the energy density of dark energy.
