  We study the nonlinear $E$-mode clustering in Lagrangian space by using large
scale structure $N$-body simulations and use the displacement field information
in Lagrangian space to recover the primordial linear density field. We find
that, compared to Eulerian nonlinear density fields, the $E$-mode displacement
fields in Lagrangian space improves the cross-correlation scale $k$ with
initial density field by a factor of 6-7, containing two orders of magnitude
more primordial information. This illustrates ability of potential density
reconstruction algorithms, to improve the baryonic acoustic oscillation
measurements from current and future large scale structure surveys.
