The $f(R)$ halo mass function in the cosmic web
  An important indicator of modified gravity is the effect of the local
environment on halo properties. This paper examines the influence of the local
tidal structure on the halo mass function, the halo orientation, spin and the
concentration-mass relation. We generalise the excursion set formalism to
produce a halo mass function conditional on large-scale structure. Our model
agrees well with simulations on large scales at which the density field is
linear or weakly non-linear. Beyond this, our principal result is that $f(R)$
does affect halo abundances, the halo spin parameter and the concentration-mass
relationship in an environment-independent way, whereas we find no appreciable
deviation from $\Lambda$CDM for the mass function with fixed environment
density, nor the alignment of the orientation and spin vectors of the halo to
the eigenvectors of the local cosmic web. There is a general trend for greater
deviation from $\Lambda$CDM in underdense environments and for high-mass
haloes, as expected from chameleon screening.
