Cosmic Voids in the SDSS DR12 BOSS Galaxy Sample: The Alcock-Paczynski test

We apply the Alcock-Paczynski (AP) test to stacked voids identified using the final data release (DR12) of the Baryon Oscillation Spectroscopic Survey (BOSS). We also use 1000 mock galaxy catalogs that match the geometry, density, and clustering properties of the BOSS sample in order to characterize the statistical uncertainties of our measurements and take into account systematic errors such as redshift space distortions. For both BOSS data and mock catalogs, we use the ZOBOV algorithm to identify voids, we stack together all voids with effective radii of 30-100 h^-1 Mpc in the redshift range of 0.43-0.7, and we accurately measure the shape of the stacked voids. Our tests with the mock catalogs show that we measure the stacked void ellipticity with a statistical precision of 2.6%. The stacked voids in redshift space are slightly squashed along the line of sight, consistent with previous studies. We repeat this measurement of stacked void shape in the BOSS data, assuming several values of ωm within the flat LCDM model, and we compare this to the mock catalogs in redshift space to perform the AP test. We obtain a constraint of ωm = -0.38_-0.15 ^+0.18 at the 68% confidence level from the AP test. We discuss the sources of statistical and systematic noise that affect the constraining power of this method. In particular, we find that the measured ellipticity of stacked voids changes more weakly with cosmology than the standard AP prediction, leading to significantly weaker constraints. We discuss how constraints will improve in future surveys with larger volumes and densities.