Large-scale structure challenges dilaton gravity in a 5D brane scenario
  with AdS bulk
  We study a theory of dilaton gravity in a 5-dimensional brane scenario, with
a non-minimal coupling of the dilaton to the matter content of the universe
localized on the brane. The effective gravitational equations at the brane are
derived in the Einstein frame in the covariant approach, addressing certain
misconceptions in the literature. We then investigate whether the observed
large-scale structure of the universe can exist on the brane in this dilaton
gravity scenario with an exact anti de Sitter bulk, assuming that the matter
energy-momentum tensor has the form of an inhomogeneous perfect fluid. The
corresponding constraint on the spatial derivative of the matter energy density
is derived, and subsequently quantified using the current limits resulting from
searches for variation of the Newton's constant. By confronting it with the
observational data from galaxy surveys, we show that up to scales of the order
of 10^4 Mpc, the derived bound on the spatial derivative of the matter energy
density does not allow for the existence of the large-scale structure as
observed today. Thus, such a dilaton gravity brane scenario is ruled out.
