Gravity's Islands: Parametrizing Horndeski Stability
  Cosmic acceleration may be due to modified gravity, with effective field
theory or property functions describing the theory. Connection to cosmological
observations through practical parametrization of these functions is difficult
and also faces the issue that not all assumed time dependence or parts of
parameter space give a stable theory. We investigate the relation between
parametrization and stability in Horndeski gravity, showing that the results
are highly dependent on the function parametrization. This can cause
misinterpretations of cosmological observations, hiding and even ruling out key
theoretical signatures. We discuss approaches and constraints that can be
placed on the property functions and scalar sound speed to preserve some
observational properties, but find that parametrizations closest to the
observations, e.g. in terms of the gravitational strengths, offer more robust
physical interpretations. In addition we present an example of how future
observations of the B-mode polarization of the cosmic microwave background from
primordial gravitational waves can probe different aspects of gravity.
