Cosmological Parameter Estimation Using the Genus Amplitude - Application to Mock Galaxy Catalogs

TL;DR

This paper explores using the genus amplitude of the matter density field in galaxy catalogs to estimate cosmological parameters, particularly dark energy and matter density, by analyzing topological features across redshifts.

Contribution

It introduces a novel method leveraging genus amplitude constancy and its evolution to constrain dark energy and matter density with mock galaxy data.

Findings

Genus amplitude remains approximately constant with redshift, serving as a standard population.

Constraints on dark energy equation of state w_de with about 15% accuracy.

Potential to constrain matter density parameter Ω_mat to within 0.01.

Abstract

We study the topology of the matter density field in two dimensional slices, and consider how we can use the amplitude $A$ of the genus for cosmological parameter estimation. Using the latest Horizon Run 4 simulation data, we calculate the genus of the smoothed density field constructed from lightcone mock galaxy catalogs. Information can be extracted from the amplitude of the genus by considering both its redshift evolution and magnitude. The constancy of the genus amplitude with redshift can be used as a standard population, from which we derive constraints on the equation of state of dark energy $w_{\rm de}$ - by measuring $A$ at $z \sim 0.1$ and $z \sim 1$, we can place an order $\Delta w_{\rm de} \sim {\cal O}(15\%)$ constraint on $w_{\rm de}$. By comparing $A$ to its Gaussian expectation value we can potentially derive an additional stringent constraint on the matter density $\Delta \Omega_{\rm mat} \sim 0.01$. We discuss the primary sources of contamination associated with the two measurements - redshift space distortion and shot noise. With accurate knowledge of galaxy bias, we can successfully remove the effect of redshift space distortion, and the combined effect of shot noise and non-linear gravitational evolution is suppressed by smoothing over suitably large scales $R_{\rm G} \ge 15 {\rm Mpc}/h$. Without knowledge of the bias, we discuss how joint measurements of the two and three dimensional genus can be used to constrain the growth factor $\beta = f/b$. The method can be applied optimally to redshift slices of a galaxy distribution generated using the drop-off technique.