Capturing primordial non-Gaussian signatures in the late Universe by multi-scale 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), and forecast their constraining power on PNG amplitudes ˡocal, fNLᵉquil,fNLᵒrtho\ and standard cosmological parameters based on ten thousands of density fields drawn from {Quijote} and {Quijote-PNG} simulations at $z=0$. With the Fisher analysis, we find that the scale-PKHF and scale-VLYDF are capable of capturing a wealth of primordial information about the Universe. Specifically, the constraint on the scalar spectral index nₛ obtained from the scale-VLYDF (scale-PKHF) is 12.4 (8.6) times tighter than that from the power spectrum, and 3.9 (2.7) times tighter than that from the bispectrum. The combination of the two statistics yields constraints on ˡocal, fNLᵉquil\ similar to those from the bispectrum and power spectrum combination, but provides a 1.4-fold improvement in the constraint on fNLᵒrtho. After including the power spectrum, its constraining power well exceeds that of the bispectrum and power spectrum combination by factors of 1.1--2.9 for all parameters.