Excursion set peaks: the role of shear
  Recent analytical work on the modelling of dark halo abundances and
clustering has demonstrated the advantages of combining the excursion set
approach with peaks theory. We extend these ideas and introduce a model of
excursion set peaks that incorporates the role of initial tidal effects or
shear in determining the gravitational collapse of dark haloes. The model -- in
which the critical density threshold for collapse depends on the tidal
influences acting on protohaloes -- is well motivated from ellipsoidal collapse
arguments and is also simple enough to be analytically tractable. We show that
the predictions of this model are in very good agreement with measurements of
the halo mass function and traditional scale dependent halo bias in N-body
simulations across a wide range of masses and redshift. The presence of shear
in the collapse threshold means that halo bias is naturally predicted to be
nonlocal, and that protohalo densities at fixed mass are naturally predicted to
have Lognormal-like distributions. We present the first direct estimate of
Lagrangian nonlocal bias in N-body simulations, finding broad agreement with
the model prediction. Finally, the simplicity of the model (which has
essentially a single free parameter) opens the door to building efficient and
accurate non-universal fitting functions of halo abundances and bias for use in
precision cosmology.
