Beyond the growth rate of cosmic structure: Testing modified gravity
  models with an extra degree of freedom
  In 'modified' gravity the observed acceleration of the universe is explained
by changing the gravitational force law or the number of degrees of freedom in
the gravitational sector. Both possibilities can be tested by measurements of
cosmological structure formation. In this paper we elaborate the details of
such tests using the Galileon model as a case study. We pay attention to the
possibility that each new degree of freedom may have stochastically independent
initial conditions, generating different types of potential well in the early
universe and breaking complete correlation between density and velocity power
spectra. This 'stochastic bias' can confuse schemes to parametrize the
predictions of modified gravity models, such as the use of the growth parameter
f alone. Using data from the WiggleZ Dark Energy Survey we show that it will be
possible to obtain constraints using information about the cosmological-scale
force law embedded in the multipole power spectra of redshift-space
distortions. As an example, we obtain an upper limit on the strength of the
conformal coupling to matter in the cubic Galileon model, giving |1/M| < 200 /
Mp. This allows the fifth-force to be stronger than gravity, but is consistent
with zero coupling.
