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 \fNLˡocal, 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 \fNLˡocal, 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.