Abstract
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.