Capturing primordial non-Gaussian signatures in the late Universe by multiscale extrema of the cosmic log-density field

We construct two new summary statistics, the scale-dependent peak height function (scale-PKHF) and the scale-dependent valley depth function (scale-VLYDF) of matter density, and forecast their constraining power on primordial non-Gaussianity and cosmological parameters based on quijote and quijote-png simulations at $z=0$. With the Fisher analysis, we demonstrate that these statistics outperform the power spectrum and bispectrum. Key findings include: (1) the constraint on the scalar spectral index ${n}_{s}$ obtained from the scale-VLYDF/scale-PKHF is $1.59/1.10$ times tighter than that from the joint analysis of power spectrum and bispectrum; (2) the combination of the two statistics yields a slight improvement in constraining ${{f}_{\mathrm{NL}}^{\text{local}},{f}_{\mathrm{NL}}^{\text{equil}}}$ over the power spectrum-bispectrum combination, and provides a 1.39-fold improvement in the constraint on ${f}_{\mathrm{NL}}^{\text{ortho}}$; and (3) after incorporating the power spectrum with our new statistics, parameter constraints surpass those from power spectrum-bispectrum combination by factors up to 2.93. This work offers an effective scheme for extracting primordial signals from the late Universe, paving the way for further breakthroughs in precision cosmology.