Galaxy Bias and $\sigma_8$ from Counts in Cells from the SDSS Main Sample

TL;DR

This paper develops a theory for galaxy counts-in-cells distribution to simultaneously measure the matter fluctuation amplitude $\sigma_8$ and galaxy bias $b$, breaking their degeneracy on large scales, and applies it to SDSS data.

Contribution

The paper introduces a new method to disentangle $\sigma_8$ and galaxy bias using counts-in-cells, validated on simulations and applied to SDSS data.

Findings

Measured $\sigma_8 = 0.94^{+.11}_{-.10}$

Estimated galaxy bias $b = 1.36^{+.14}_{-.11}$

Results are consistent with previous measurements

Abstract

The counts-in-cells (CIC) galaxy probability distribution depends on both the dark matter clustering amplitude $\sigma_8$ and the galaxy bias $b$. We present a theory for the CIC distribution based on a previous prescription of the underlying dark matter distribution and a linear volume transformation to redshift space. We show that, unlike the power spectrum, the CIC distribution breaks the degeneracy between $\sigma_8$ and $b$ on scales large enough that both bias and redshift distortions are still linear; thus we obtain a simultaneous fit for both parameters. We first validate the technique on the Millennium Simulation and then apply it to the SDSS Main Galaxy Sample. We find $\sigma_8 = 0.94^{+.11}_{-.10}$ and $b = 1.36^{+.14}_{-.11}$, consistent with previous complementary results from redshift distortions and from Planck.