Galaxy Bias and ${\sigma }_8$ from Counts in Cells from the SDSS Main Sample

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 ${\sigma }_8=0.94_{-.10}^{+.11}$ and $b=1.36_{-.11}^{+.14}$, consistent with previous complementary results from redshift distortions and from Planck.

5 pages, 3 figures; submitted to MNRAS

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