Testing gravity with halo density profiles observed through
  gravitational lensing
  We present a new test of the modified gravity endowed with the Vainshtein
mechanism with the density profile of a galaxy cluster halo observed through
gravitational lensing. A scalar degree of freedom in the galileon modified
gravity is screened by the Vainshtein mechanism to recover Newtonian gravity in
high-density regions, however it might not be completely hidden on the outer
side of a cluster of galaxies. Then the modified gravity might yield an
observational signature in a surface mass density of a cluster of galaxies
measured through gravitational lensing, since the scalar field could contribute
to the lensing potential. We investigate how the transition in the Vainshtein
mechanism affects the surface mass density observed through gravitational
lensing, assuming that the density profile of a cluster of galaxies follows the
original Navarro-Frenk-White (NFW) profile, the generalized NFW profile and the
Einasto profile. We compare the theoretical predictions with observational
results of the surface mass density reported recently by other researchers. We
obtain constraints on the amplitude and the typical scale of the transition in
the Vainshtein mechanism in a subclass of the generalized galileon model.
