Tidal shear and the consistency of microscopic Lagrangian halo approaches

Understand

We delineate the conditions under which the consistency relation for the non-Gaussian bias and the universality of the halo mass function hold in the context of microscopic Lagrangian descriptions of halos.

• The former is valid provided that the collapse barrier depends only on the physical fields (instead of fields normalized by their variance for example) and explicitly includes the effect of {\it all} physical fields such as the tidal shear.
• The latter holds provided that the response of the halo number density to a long-wavelength density fluctuation is equivalent to the response induced by shifting the spherical collapse threshold.
• Our results apply to any Lagrangian halo bias prescription.