What does the Marked Power Spectrum Measure? Insights from Perturbation Theory

Abstract

The marked power spectrum is capable of placing far tighter constraints on cosmological parameters (particularly the neutrino mass) than the conventional power spectrum. What new information does it contain beyond conventional statistics? Through the development of a perturbative model, we find that the mark induces a significant coupling between small-scale non-Gaussianities and large scales, leading to the additional information content. The model is derived in the context of oneloop perturbation theory and validated by comparison to N -body simulations across a variety of mark parameters. At moderate redshifts, including for massive neutrino cosmologies, the theory is in good agreement with the simulations. The mixing of large and small scales complicates the modeling as there is no well-defined convergence radius of the theory at low z. Extension to higher perturbative order and biased tracers is possible via a similar approach, and a simple model of the latter is shown to yield promising results. The theory becomes non-perturbative at redshift zero for small smoothing scales. This suggests that marked spectrum may have important contributions from baryonic effects even at low k: these will need to be studied before the full power of this tool can be realized.

The effect of finite halo size on the clustering of neutral hydrogen

“…For tracers of dark matter, the validity scales are different but qualitatively follow the same pattern. On linear-theory scales, k < k NL , there are important beyond-linear corrections for tracers, since clustering on these scales is sensitive to clustering on smaller scales [18,35].…”

Using the Mark Weighted Correlation Functions to Improve the Constraints on Cosmological Parameters

“…MCF are also computationally efficient compared with the high order statistics, like the 3pCF. Philcox et al (2020) used perturbation theory to study the marked power spectrum using perturbation theory, and found that the mark introduces a significant coupling between small-scale non-Gaussianities and large scale clustering. This explains why using this statistics we can get additional information, and provides further support to the findings of this work.…”

“…Ongoing research seeks to go beyond the 2-point statistics includes the methods such as 3-point statistics (Sabiu et al 2016;Slepian et al 2017), 4-point statistics (Sabiu et al 2019), cosmic voids (Ryden 1995a;Lavaux & Wandelt 2012a), deep learning (Ravanbakhsh et al 2017;Mathuriya et al 2018), and so on. While many of them have proved useful, here we investigate another statistical tool, namely the mark weighted correlation function (MCF; Beisbart & Kerscher 2000;Beisbart et al 2002;Gottlöber et al 2002;Sheth & Tormen 2004;Sheth et al 2005;Skibba et al 2006;White & Padmanabhan 2009;Satpathy et al 2019;Massara et al 2020;Philcox et al 2020) which is simpler and computationally easier compared than the statistics mentioned above.…”

Constraining primordial non-Gaussianity from large scale structure with the wavelet scattering transform

“…With such goals in mind, several NG summaries have already been considered in LSS analysis. Among those, let us mention for example marked spectra [6][7][8][9][10], power spectra from cosmic web environments [11,12], skew spectra [13][14][15][16], Minkowski functionals [17,18], k-nearest neighbour cumulative distributions functions [19,20], probability distribution function (PDF) of late-time cosmic density fluctuations [21,22], halo mass function probes [23][24][25][26][27][28], and the void abundance [29,30].…”