Nonlinear $E$-mode clustering in Lagrangian space

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.