The galaxies in our Universe form inside the potential wells of virialized dark matter structures, since only there baryons can cool efficiently. Furthermore, the non-linear density profiles around haloes determine the small scale matter power spectrum, which in turn affects gravitational lensing.
We would thus like to understand where haloes form (their initial conditiona) and how they evolve. The seeds for all the rich structure we observe today where already present in the linear and highly Gaussian initial density fields. It is thus instructive to understand where in this Gaussian field haloes will form.
The peak model selects maxima of this Gaussian or weakly non-Gaussian field. This goes beyond the usual thresholding that is performed in the local bias model, since constraints on the first and second derivatives of the field are employed to select peaks.
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