The Shape Dependence of Vainshtein Screening in the Cosmic Matter
  Bispectrum
  One of the most pressing questions in modified gravity is how deviations from
general relativity can manifest in upcoming galaxy surveys. This is especially
relevant for theories exhibiting Vainshtein screening, where such deviations
are efficiently suppressed within a (typically large) Vainshtein radius.
However, Vainshtein screening is known to be shape dependent: it is most
effective around spherical sources, weaker around cylindrical objects and
completely absent for planar sources. The Cosmic Web therefore offers a testing
ground, as it displays many shapes in the form of clusters, filaments and
walls.
  In this work, we explicitly derive the signature of the shape dependence of
Vainshtein screening on the matter bispectrum, by considering a cubic Galileon
model with a conformal coupling to matter and a cosmological constant. We
perform a second order perturbative analysis, deriving analytic, integral
expressions for the bispectrum, which we integrate using hi_class. We find that
the shape dependence of Vainshtein screening enters the bispectrum with a
unique scale-factor dependence of $\propto a^{3/2}$. The magnitude of the
effect today is up to 2 % for a model whose linear growth rate deviates up to 5
% from $\Lambda$CDM.
