Constraints on Chameleon f(R)-Gravity from Galaxy Rotation Curves of the
  SPARC Sample
  In chameleon $f(R)$-gravity, the fifth force will lead to `upturns' in galaxy
rotation curves near the screening radius. The location of the upturn depends
on the cosmic background value of the scalar field $f_{R0}$, as well as the
mass, size and environment of the galaxy. We search for this signature of
modified gravity in the SPARC sample of measured rotation curves, using an MCMC
technique to derive constraints on $f_{R0}$. Assuming NFW dark matter haloes
and with $f_{R0}$ freely varying for each galaxy, most galaxies prefer $f(R)$
gravity to $\Lambda$CDM, but there is a large spread of inferred $f_{R0}$
values, inconsistent with a single global value. Requiring instead a consistent
$f_{R0}$ value for the whole sample, models with $\log_{10}|f_{R0}| > -6.1$ are
excluded. On the other hand, models in the range $-7.5<\log_{10}|f_{R0}|<-6.5$
seem to be favoured with respect to $\Lambda$CDM, with a significant peak at
-7. However, this signal is largely a result of galaxies for which the $f(R)$
signal is degenerate with the core/cusp problem, and when the NFW profile is
replaced with a cored halo profile, $\Lambda$CDM gives better fits than any
given $f(R)$ model. Thus, we find no convincing evidence of $f(R)$ gravity down
to the level of $|f_{R0}| \sim 6 \times 10^{-8}$, with the caveat that if cored
halo density profiles cannot ultimately be explained within $\Lambda$CDM, a
screened modified gravity theory could possibly provide an alternative solution
for the core/cusp problem. However, the $f(R)$ models studied here fall short
of achieving this.
