Galaxy morphology rules out astrophysically relevant Hu-Sawicki $f(R)$
  gravity
  $f(R)$ is a paradigmatic modified gravity theory that typifies extensions to
General Relativity with new light degrees of freedom and hence screened fifth
forces between masses. These forces produce observable signatures in galaxy
morphology, caused by a violation of the weak equivalence principle due to a
differential impact of screening among galaxies' mass components. We compile
statistical datasets of two morphological indicators -- offsets between stars
and gas in galaxies and warping of stellar disks -- and use them to constrain
the strength and range of a thin-shell-screened fifth force. This is achieved
by applying a comprehensive set of upgrades to past work (Desmond et al
2018a,b): we construct a robust galaxy-by-galaxy Bayesian forward model for the
morphological signals, including full propagation of uncertainties in the input
quantities and marginalisation over an empirical model describing astrophysical
noise. Employing more stringent data quality cuts than previously we find no
evidence for a screened fifth force of any strength $\Delta G/G_\text{N}$ in
the Compton wavelength range $0.3-8$ Mpc, setting a $1\sigma$ bound of $\Delta
G/G_\text{N}<0.8$ at $\lambda_C=0.3$ Mpc that strengthens to $\Delta
G/G_\text{N}<3\times10^{-5}$ at $\lambda_C=8$ Mpc. These are the tightest
bounds to date beyond the Solar System by over an order of magnitude. For the
Hu-Sawicki model of $f(R)$ with $n=1$ we require a background scalar field
value $f_{R0} < 1.4 \times 10^{-8}$, forcing practically all astrophysical
objects to be screened. We conclude that this model can have no relevance to
astrophysics or cosmology.
