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 $\eta$ 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 $P_{\mathrm{Z}\mathrm{I},0}$, constructed from three representative transforms with $\eta =1$, $10$, and $+\mathrm{\infty }$, yields substantially tighter constraints than the conventional halo power spectrum $P_{\mathrm{h},0}$ 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 $P_{\mathrm{Z}\mathrm{I},0}$ improves the constraints on $f_{\mathrm{N}\mathrm{L}}^{\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{l}}$, $f_{\mathrm{N}\mathrm{L}}^{\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{h}\mathrm{o}}$, $M_{\nu }$, and $n_{\mathrm{s}}$ by factors of $5.6$, $5.5$, $5.2$, and $5.8$, respectively, relative to $P_{\mathrm{h},0}$. 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.