Halo bias in the peak model. A first-principles non-parametric approach

The Press-Schechter (PS) and excursion set (ES) models of structure formation fail in reproducing the halo bias found in simulations, while the excursion set-peaks (ESP) formalism built in the peak model reproduces it only at high masses and does not address in a fully satisfactory manner peak nesting and the mass and time of ellipsoidal collapse of triaxial peaks in the Gaussian-smoothed density field. Here we apply the CUSP formalism fixing all these issues from first principles and with no free parameters to infer the Lagrangian local peak bias parameters, which adopt very simple analytic expressions similar to those found in the PS and ES models. The predicted Eulerian linear halo bias recovers the results of simulations. More specifically, we show that the only small departure observed at intermediate and low masses can be due to the spurious halo splitting and grouping caused by the Spherical Overdensity halo-finding algorithm used in simulations.