Local Nonlinear Transforms effectively Reveal Primordial Information in Large-Scale Structure

To eliminate gravitational non-Gaussianity, we introduce the $\mathcal{Z}$-$\kappa$ transform, a simple local nonlinear transform of the matter density field that emulates the inverse of nonlinear gravitational evolution. Using $N$-body simulations, we show that the $\mathcal{Z}$-$\kappa$ transform with $\kappa =6$ or $\kappa \to \mathrm{\infty }$ (i.e., log) substantially Gaussianizes the density distribution, and recovers the linear power spectrum. In an extended parameter space including primordial non-Gaussianity, summed neutrino mass, and $\mathrm{\Lambda }$CDM parameters, Fisher analysis demonstrates that power spectra of transformed fields provide strong complementary constraints. A central result is that these power spectra can directly capture the local primordial non-Gaussianity imprinted in large-scale structure. This opens a new avenue for probing the physics of the early Universe with Stage-IV surveys using two-point statistics.