Forecasting cosmological constraints from the nonlinear halo density field with Zel'dovich-inspired transform

The Zel'dovich-inspired (ZI) transform is a local nonlinear transform of the density field that can Gaussianize the late-time matter field and recover information from higher-order N-point correlation functions through its power spectrum, with the parameter η controlling the weighting of higher-order information. Using Fisher-matrix analyses of halo catalogs from the Quijote and Quijote-PNG simulations, we study the redshift-space monopole power spectrum of the ZI-transformed halo density field. The joint statistic P ZI,0, constructed from three representative transforms with η=1, 10, and + infinity, yields substantially tighter constraints than the conventional halo power spectrum P h,0 on standard cosmological parameters, the summed neutrino mass, and primordial non-Gaussianity amplitudes, while outperforming the marked power spectrum for many parameters. We further calibrate a scale-dependent noise correction for the ZI power spectrum, with an effective noise amplitude that depends on wavenumber, and find that the correction further tightens the constraints. In particular, the noise-corrected P ZI,0 improves the constraints on f NL equil, f NL ortho, M ν, and n s by factors of 5.6, 5.5, 5.2, and 5.8, respectively, relative to P h,0. These results demonstrate the potential of ZI power spectra as a complement to standard two-point statistics for extracting nonlinear cosmological information. Our forecasts may be conservative because the halo catalogs have substantially lower number densities than those expected from forthcoming galaxy surveys.