The constraining power of the Marked Power Spectrum: an analytical study

TL;DR

This paper provides the first comprehensive analytical study of the marked power spectrum's sensitivity to primordial non-Gaussianity, comparing its constraining power to traditional methods and exploring optimal mark parameters.

Contribution

It extends effective field theory to include primordial non-Gaussianity, validating a theoretical model against simulations and analyzing the practical advantages of the marked power spectrum.

Findings

Marked power spectrum constrains primordial non-Gaussianity effectively in certain regimes.

Performance for discrete tracers with BOSS-like densities does not surpass traditional P+B analysis at mildly non-linear scales.

Marked statistics offer practical benefits like simpler estimation and systematic control.

Abstract

The marked power spectrum - a two-point correlation function of a transformed density field - has emerged as a promising tool for extracting cosmological information from the large-scale structure of the Universe. In this work, we present the first comprehensive analytical study of the marked power spectrum's sensitivity to primordial non-Gaussianity (PNG) of the non-local type. We extend previous effective field theory frameworks to incorporate PNG, developing a complete theoretical model that we validate against the Quijote simulation suite. Through a systematic Fisher analysis, we compare the constraining power of the marked power spectrum against traditional approaches combining the power spectrum and bispectrum (P+B). We explore different choices of mark parameters to evaluate their impact on parameter constraints, particularly focusing on equilateral and orthogonal PNG as well as neutrino masses. Our analysis shows that while marking up underdense regions yields optimal constraints in the low shot-noise regime, the marked power spectrum's performance for discrete tracers with BOSS-like number densities does not surpass that of P+B analysis at mildly non-linear scales ($k \lesssim 0.25 \,h/\text{Mpc}$). However, the marked approach offers several practical advantages, including simpler estimation procedures and potentially more manageable systematic effects. Our theoretical framework reveals how the marked power spectrum incorporates higher-order correlation information through terms resembling tree-level bispectra and power spectrum convolutions. This work establishes a robust foundation for applying marked statistics to future large-volume surveys.