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

We present measurements of the two-dimensional genus of the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS) catalogs to constrain cosmological parameters governing the shape of the matter power spectrum. The BOSS data are divided into 12 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 nonlinear gravitational collapse. The genus amplitude provides a measure of the shape of the linear matter power spectrum and is principally sensitive to ch2 and scalar spectral index ns. A strong negative degeneracy between ch2 and ns is observed, as both can increase small-scale power by shifting the peak and tilting the power spectrum, respectively. We place a constraint on the particular combination -we find after combining the LOWZ and CMASS data sets, assuming a flat ΛCDM cosmology. This result is practically insensitive to reasonable variations of the power spectrum amplitude and linear galaxy bias. Our results are consistent with the Planck best fit .