Cosmological Parameter Estimation from the Two-Dimensional Genus Topology -- Measuring the Expansion History using the Genus Amplitude as a Standard Ruler

TL;DR

This paper uses the genus topology of galaxy distributions in SDSS-III BOSS data across different redshifts to constrain cosmological parameters, providing a novel standard ruler method for measuring the Universe's expansion history.

Contribution

It introduces a new approach using the genus amplitude as a conserved quantity across redshifts to constrain dark energy and matter density parameters.

Findings

Measured genus in 12 redshift shells from SDSS-III BOSS.

Constrained dark energy equation of state to w_de = -1.05^{+0.13}_{-0.12}.

Estimated matter density parameter to be Ω_m = 0.303 ± 0.036.

Abstract

We measure the genus of the galaxy distribution in two-dimensional slices of the SDSS-III BOSS catalog to constrain the cosmological parameters governing the expansion history of the Universe. The BOSS catalogs are divided into twelve concentric shells over the redshift range $0.25 < z < 0.6$ and we repeatedly measure the genus from the two-dimensional galaxy density fields, each time varying the cosmological parameters used to infer the distance-redshift relation to the shells. We also indirectly reconstruct the two-dimensional genus amplitude using the three-dimensional genus measured from SDSS Main Galaxy Sample with galaxies at low redshift $z < 0.12$. We combine the low- and high-redshift measurements, finding the cosmological model which minimizes the redshift evolution of the genus amplitude, using the fact that this quantity should be conserved. Being a distance measure, the test is sensitive to the matter density parameter ($\Omega_{\rm m}$) and equation of state of dark energy ($w_{\rm de}$). We find a constraint of $w_{\rm de} = -1.05^{+0.13}_{-0.12}$, $\Omega_{\rm m} = 0.303 \pm 0.036$ after combining the high- and low-redshift measurements and combining with Planck CMB data. Higher redshift data and combining data sets at low redshift will allow for stronger constraints.