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We apply the Alcock-Paczynski (AP) test to the stacked voids identified usingthe large-scale structure galaxy catalog from the Baryon OscillationSpectroscopic Survey (BOSS). This galaxy catalog is part of the Sloan DigitalSky Survey (SDSS) Data Release 12 and is the final catalog of SDSS-III. We alsouse 1000 mock galaxy catalogs that match the geometry, density, and clusteringproperties of the BOSS sample in order to characterize the statisticaluncertainties of our measurements and take into account systematic errors suchas redshift space distortions. For both BOSS data and mock catalogs, we use theZOBOV algorithm to identify voids, we stack together all voids with effectiveradii of 30-100Mpc/h in the redshift range 0.43-0.7, and we accurately measurethe shape of the stacked voids. Our tests with the mock catalogs show that wemeasure the stacked void ellipticity with a statistical precision of 2.6%. Wefind that the stacked voids in redshift space are slightly squashed along theline of sight, which is consistent with previous studies. We repeat thismeasurement of stacked void shape in the BOSS data assuming several values ofOmega_m within the flat LCDM model, and we compare to the mock catalogs inredshift space in order to perform the AP test. We obtain a constraint of$\Omega_m = 0.38^{+0.18}_{-0.15}$ at the 68% confidence level from the AP test.We discuss the various sources of statistical and systematic noise that affectthe constraining power of this method. In particular, we find that the measuredellipticity of stacked voids scales more weakly with cosmology than thestandard AP prediction, leading to significantly weaker constraints. We discusshow AP constraints will improve in future surveys with larger volumes anddensities.

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