Effect of full spherical collapse near the distribution mode

Determine how using the full spherical-collapse model, rather than the approximate linear-to-nonlinear overdensity conversion, affects the location of the mode of the double distribution near the mode’s density value.

Background

The paper compares an approximate spherical-collapse conversion between the linearly extrapolated overdensity and the nonlinear matter density with a numerically implemented full spherical-collapse conversion. Numerical stiffness near the lower density bound prevents the authors from resolving the full conversion in the density range containing the distribution modes.

Although the approximate conversion agrees with the full conversion to within a few percent over the resolvable range, the effect of the full conversion on the mode itself remains unresolved. Establishing this effect would clarify whether the spherical-collapse approximation contributes materially to the predicted most-probable outer density profile.