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

TL;DR

This paper demonstrates that using mark weighted correlation functions (MCFs) with various density weightings enhances the precision of cosmological parameter constraints, especially for parameters like _m and w, by combining different MCF types.

Contribution

The study introduces a comprehensive analysis of multiple MCFs with different density weightings, showing their potential to significantly improve constraints on cosmological parameters over standard correlation functions.

Findings

Different MCFs exhibit distinct amplitudes and scale-dependence.

Combining multiple MCFs improves constraints on _m and w by up to 50%.

Features in MCFs can probe structure formation parameters like _8 and galaxy bias.

Abstract

We used the mark weighted correlation functions (MCFs), $W(s)$, to study the large scale structure of the Universe. We studied five types of MCFs with the weighting scheme $\rho^\alpha$, where $\rho$ is the local density, and $\alpha$ is taken as $-1,\ -0.5,\ 0,\ 0.5$, and 1. We found that different MCFs have very different amplitudes and scale-dependence. Some of the MCFs exhibit distinctive peaks and valleys that do not exist in the standard correlation functions. Their locations are robust against the redshifts and the background geometry, however it is unlikely that they can be used as ``standard rulers'' to probe the cosmic expansion history. Nonetheless we find that these features may be used to probe parameters related with the structure formation history, such as the values of $\sigma_8$ and the galaxy bias. Finally, after conducting a comprehensive analysis using the full shapes of the $W(s)$s and $W_{\Delta s}(\mu)$s, we found that, combining different types of MCFs can significantly improve the cosmological parameter constraints. Compared with using only the standard correlation function, the combinations of MCFs with $\alpha=0,\ 0.5,\ 1$ and $\alpha=0,\ -1,\ -0.5,\ 0.5,\ 1$ can improve the constraints on $\Omega_m$ and $w$ by $\approx30\%$ and $50\%$, respectively. We find highly significant evidence that MCFs can improve cosmological parameter constraints.