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

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 ρ α , where ρ is the local density, and α 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 σ 8 and the galaxy bias. Finally, after conducting a comprehensive analysis using the full shapes of the W(s)s and W Δs (μ)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 α = 0, 0.5, 1 and α = 0, −1, −0.5, 0.5, 1 can improve the constraints on Ω m and w by ≈30% and 50%, respectively. We find highly significant evidence that MCFs can improve cosmological parameter constraints.

Cosmological Information in the Marked Power Spectrum of the Galaxy Field

“…The related marked power spectra will contain slightly different information and possibly present different parameter degeneracies. Thus, combinations of multiple marked power spectra of the same initial field can break degeneracies and allow retrieving even more cosmological information (Yang et al 2020;Massara et al 2021). Additionally, Xiao et al (2022) proposed the use of marks that depend on the gradient of the local density field, rather than the field itself.…”