Marked correlation functions in perturbation theory

TL;DR

This paper develops perturbation theory models for the marked correlation function to differentiate modified gravity from standard cosmology, achieving accurate predictions on quasi non-linear scales.

Contribution

It introduces a perturbation theory approach within Convolution Lagrangian Perturbation Theory to model marked correlation functions, enabling better understanding of cosmological model differences.

Findings

Perturbation theory matches N-body simulations within 1% on relevant scales.

Models accurately predict dark matter and galaxy marked correlation functions down to 30 Mpc/h.

Approaches help disentangle galaxy bias from cosmological signals.

Abstract

We develop perturbation theory approaches to model the marked correlation function constructed to up-weight low density regions of the Universe, which might help distinguish modified gravity models from the standard cosmology model based on general relativity. Working within Convolution Lagrangian Perturbation Theory, we obtain that weighted correlation functions are expressible as double convolution integrals that we approximate using a combination of Eulerian and Lagrangian schemes. We find that different approaches agree within 1$\%$ on quasi non-linear scales. Compared with {\it N}-body simulations, the perturbation theory is found to provide accurate predictions for the marked correlation function of dark matter fields, dark matter halos as well as Halo Occupation Distribution galaxies down to $30$ Mpc/h. These analytic approaches help to understand the degeneracy between the mark and the galaxy bias and find a way to maximize the differences among various cosmological models.