The initial shear field in models with primordial local non-Gaussianity and implications for halo and void abundances

Understand

We generalize Doroshkevich's celebrated formulae for the eigenvalues of the initial shear field associated with Gaussian statistics to the local non-Gaussian f_{nl} model.

• This is possible because, to at least second order in f_{nl}, distributions at fixed overdensity are unchanged from the case f_{nl}=0.
• We use this generalization to estimate the effect of f_{nl}\ne 0 on the abundance of virialized halos.
• Halo abundances are expected to be related to the probability that a certain quantity in the initial fluctuation field exceeds a threshold value, and we study two choices for this variable: it can either be the sum of the eigenvalues of the initial deformation tensor (the initial overdensity), or its smallest eigenvalue.