[Paper Review] Cosmological constraints from the density gradient weighted correlation function

Xiaoyuan Xiao, Yizhao Yang+9 more|arXiv (Cornell University)|Mar 29, 2022

Galaxies: Formation, Evolution, Phenomena109 references8 citations

TL;DR

This paper proposes a novel cosmological statistic using the density gradient weighted correlation function (W∆s(µ)) to enhance constraints on cosmological parameters beyond standard two-point statistics. By weighting galaxy clustering with |∇ρ/ρ|α, the method captures non-Gaussian structure information, showing that gradient weighting is statistically more powerful than density weighting alone, and combining both schemes improves constraints by up to 25% over gradient weighting alone, strengthening Ωm constraints by factors of 2–4 compared to the standard 2pCF.

ABSTRACT

The mark weighted correlation function (MCF) $W(s,\mu)$ is a computationally efficient statistical measure which can probe clustering information beyond that of the conventional 2-point statistics. In this work, we extend the traditional mark weighted statistics by using powers of the density field gradient $| abla ho/ ho|^\alpha$ as the weight, and use the angular dependence of the scale-averaged MCFs to constrain cosmological parameters. The analysis shows that the gradient based weighting scheme is statistically more powerful than the density based weighting scheme, while combining the two schemes together is more powerful than separately using either of them. Utilising the density weighted or the gradient weighted MCFs with $\alpha=0.5,\ 1$, we can strengthen the constraint on $\Omega_m$ by factors of 2 or 4, respectively, compared with the standard 2-point correlation function, while simultaneously using the MCFs of the two weighting schemes together can be $1.25$ times more statistically powerful than using the gradient weighting scheme alone. The mark weighted statistics may play an important role in cosmological analysis of future large-scale surveys. Many issues, including the possibility of using other types of weights, the influence of the bias on this statistics, as well as the usage of MCFs in the tomographic Alcock-Paczynski method, are worth further investigations.

Motivation & Objective

• To improve cosmological parameter constraints beyond standard two-point statistics by incorporating non-Gaussian clustering information.
• To investigate whether the spatial gradient of the density field can serve as a more informative mark than density itself in marked correlation functions.
• To assess the statistical power of combining density-based and gradient-based weighting schemes in constraining Ωm.
• To evaluate the feasibility and advantages of using gradient-weighted MCFs in future large-scale structure surveys.

Proposed method

• The study introduces a new marked correlation function (MCF) where the mark is defined as |∇ρ/ρ|α, with α = 0.5 and 1, to weight galaxy pairs based on local density gradient.
• The anisotropic, scale-averaged MCF  W∆s(µ) is computed from N-body simulations (BigMD and COLA) to capture angular dependence and redshift-space distortions.
• Cosmological constraints are derived by comparing W∆s(µ) across simulations with different Ωm values (0.25–0.35), using χ² and reduced χ² statistics.
• The method compares statistical power across three schemes: standard 2pCF, density-weighted MCF, and gradient-weighted MCF, with joint use of both weighting types.
• The analysis uses a set of 5 COLA simulations with 1024³ particles in a (680h⁻¹Mpc)³ box to ensure sufficient volume for scale-dependent clustering analysis.
• The covariance matrix is estimated from mock simulations, and statistical significance is evaluated via χ² and reduced χ², with degrees of freedom approximated as the number of points minus one.

Experimental results

Research questions

• RQ1 Can the density gradient |∇ρ/ρ|α serve as a more informative mark than the density itself in marked correlation functions for cosmological parameter estimation?
• RQ2 How does the statistical power of the gradient-weighted MCF compare to that of the standard 2pCF and the density-weighted MCF?
• RQ3 Is there a synergistic improvement when combining both density-based and gradient-based weighting schemes in MCF analysis?
• RQ4 To what extent does the gradient-weighted MCF enhance constraints on Ωm compared to standard two-point statistics?
• RQ5 How robust is the method to cosmological model assumptions and simulation systematics?

Key findings

• The gradient-weighted MCF is statistically more powerful than the density-weighted MCF, with a 25% higher statistical power than using gradient weighting alone when both are combined.
• Using the gradient-weighted MCF with α = 1 strengthens the constraint on Ωm by a factor of 4 compared to the standard 2-point correlation function.
• Using the density-weighted MCF with α = 0.5 strengthens the Ωm constraint by a factor of 2 compared to the standard 2pCF.
• Combining both density-based and gradient-based weighting schemes yields a 1.25 times higher statistical power than using the gradient weighting scheme alone.
• The χ² and reduced χ² statistics confirm that both weighting schemes can distinguish simulations with different Ωm values, with the gradient scheme showing superior discrimination.
• The method demonstrates that the density gradient captures complementary information to the density field, enhancing sensitivity to clustering patterns in different cosmic web environments.