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

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 (${\Omega }_{\mathrm{m}}$) and equation of state of dark energy ($w_{\mathrm{de}}$). We find a constraint of $w_{\mathrm{de}}=-1.05_{-0.12}^{+0.13}$, ${\Omega }_{\mathrm{m}}=0.303\pm 0.036$ 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.

arXiv commentAccepted for publication in the Astrophysical Journal. 19 pages, 13 figures

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