Challenges in Connecting Modified Gravity Theory and Observations
  Cosmic acceleration may be due to modifications of cosmic gravity and to test
this we need robust connections between theory and observations. However, in a
model independent approach like effective field theory or a broad class like
Horndeski gravity, several free functions of time enter the theory. We show
that simple parametrizations of these functions are unlikely to be successful;
in particular the approximation $\alpha_i(t)\propto\Omega_{\rm de}(t)$
drastically misestimates the observables. This holds even in simple modified
gravity theories like $f(R)$. Indeed, oversimplified approximations to the
property functions $\alpha_i(t)$ can even miss the signature of modified
gravity. We also consider the question of consistency relations and the role of
tensor (gravitational wave) perturbations.
