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

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 theW(s)s andW(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)andwby 30% and 50%, respectively. We find highly significant evidence that MCFs can improve cosmological parameter constraints.