We apply the Alcock-Paczyński ( AP ) test to the stacked voids identified using the large-scale structure galaxy catalog from the Baryon Oscillation Spectroscopic Survey ( BOSS ) .
This galaxy catalog is part of the Sloan Digital Sky Survey Data Release 12 and is the final catalog of SDSS-III .
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 } \mathrm { Mpc } in the redshift range 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 , which is consistent with previous studies .
We repeat this measurement of stacked void shape in the BOSS data assuming several values of \Omega _ { \mathrm { m } } within the flat \Lambda \mathrm { CDM } model , and we compare to the mock catalogs in redshift space in order to perform the AP test .
We obtain a constraint of \Omega _ { \mathrm { 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 affect the constraining power of this method .
In particular , we find that the measured ellipticity of stacked voids scales more weakly with cosmology than the standard AP prediction , leading to significantly weaker constraints .
We discuss how AP constraints will improve in future surveys with larger volumes and densities .