Constrained simulations and excursion sets: understanding the risks and
  benefits of `genetically modified' haloes
  Constrained realisations of Gaussian random fields are used in cosmology to
design special initial conditions for numerical simulations. We review this
approach and its application to density peaks providing several worked-out
examples. We then critically discuss the recent proposal to use constrained
realisations to modify the linear density field within and around the
Lagrangian patches that form dark-matter haloes. The ambitious concept is to
forge `genetically modified' haloes with some desired properties after the
non-linear evolution. We demonstrate that the original implementation of this
method is not exact but approximate because it tacitly assumes that protohaloes
sample a set of random points with a fixed mean overdensity. We show that
carrying out a full genetic modification is a formidable and daunting task
requiring a mathematical understanding of what determines the biased locations
of protohaloes in the linear density field. We discuss approximate solutions
based on educated guesses regarding the nature of protohaloes. We illustrate
how the excursion-set method can be adapted to predict the non-linear evolution
of the modified patches and thus fine tune the constraints that are necessary
to obtain preselected halo properties. This technique allows us to explore the
freedom around the original algorithm for genetic modification. We find that
the quantity which is most sensitive to changes is the halo mass-accretion rate
at the mass scale on which the constraints are set. Finally we discuss
constraints based on the protohalo angular momenta.
