Cosmological Parameter Estimation from the Two-Dimensional Genus Topology -- Measuring the Shape of the Matter Power Spectrum

Understand

We present measurements of the two-dimensional genus of the SDSS-III BOSS catalogs to constrain cosmological parameters governing the shape of the matter power spectrum.

• The BOSS data are divided into twelve concentric shells over the redshift range $0.2 < z < 0.6$, and we extract the genus from the projected two-dimensional galaxy density fields.
• We compare the genus amplitudes to their Gaussian expectation values, exploiting the fact that this quantity is relatively insensitive to non-linear gravitational collapse.
• The genus amplitude provides a measure of the shape of the linear matter power spectrum, and is principally sensitive to $\Omega_{\rm c}h^{2}$ and scalar spectral index $n_{\rm s}$.