Consistency relations for large-scale structure in modified gravity and
  the matter bispectrum
  We study perturbation theory for large-scale structure in the most general
scalar-tensor theories propagating a single scalar degree of freedom, which
include Horndeski theories and beyond. We model the parameter space using the
effective field theory of dark energy. For Horndeski theories, the
gravitational field and fluid equations are invariant under a combination of
time-dependent transformations of the coordinates and fields. This symmetry
allows one to construct a physical adiabatic mode which fixes the
perturbation-theory kernels in the squeezed limit and ensures that the
well-known consistency relations for large-scale structure, originally derived
in general relativity, hold in modified gravity as well. For theories beyond
Horndeski, instead, one generally cannot construct such an adiabatic mode.
Because of this, the perturbation-theory kernels are modified in the squeezed
limit and the consistency relations for large-scale structure do not hold. We
show, however, that the modification of the squeezed limit depends only on the
linear theory. We investigate the observational consequences of this violation
by computing the matter bispectrum. In the squeezed limit, the largest effect
is expected when considering the cross-correlation between different tracers.
Moreover, the individual contributions to the 1-loop matter power spectrum do
not cancel in the infrared limit of the momentum integral, modifying the power
spectrum on non-linear scales.
