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  • Open Access

Optimal marked statistics from the effective field theory of large scale structure

Marco Marinucci1,2,3, Michele Liguori2,3, Federico Semenzato2,3, and Benjamin D. Wandelt4,5

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Phys. Rev. D 114, 083508 – Published 6 October, 2026

DOI: https://doi.org/10.1103/3bqt-5fyk

Abstract

We present a simple and robust framework to assess the information content of the power spectrum of a marked dark matter density field within the effective field theory of large scale structure, providing a physically motivated regime of validity of perturbation theory for such fields. We optimize the choice of mark to maximize the constraining power on cosmological parameters, focusing on the resulting reduction of parameter uncertainties. After marginalizing over the small-scale counterterms, we find improvements in the parameter error bars by a factor of approximately 1.30–2.3, 1.3–8.3, and 1.2–2.5 for Ωm, σ8, and h, respectively, depending on redshift and smoothing scale. The optimized mark exhibits a simple functional form, for which we provide a physical interpretation in terms of its response to the underlying density field. The results presented in this work, which are valid for dark matter in real space, demonstrate the potential of marked statistics as a tool to extract additional cosmological information beyond standard two-point analyses and open a pathway for further exploration of nonlinear transformations of the density field.

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Phys. Rev. D 114, 083508– Published 6 October, 2026
  • Received 10 July 2026
  • Accepted 10 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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