Measuring baryon acoustic oscillations from the clustering of voids

We investigate the necessary methodology to optimally measure the baryon acoustic oscillation (BAO) signal from voids, based on galaxy redshift catalogues. To this end, we study the dependence of the BAO signal on the population of voids classified by their sizes. We find for the first time the characteristic features of the correlation function of voids including the first robust detection of BAOs in mock galaxy catalogues. These show an anti-correlation around the scale corresponding to the smallest size of voids in the sample (the void exclusion effect), and dips at both sides of the BAO peak, which can be used to determine the significance of the BAO signal without any priori model. Furthermore, our analysis demonstrates that there is a scale-dependent bias for different populations of voids depending on the radius, with the peculiar property that the void population with the largest BAO significance corresponds to tracers with approximately zero bias on the largest scales. We further investigate the methodology on an additional set of 1000 realistic mock galaxy catalogues reproducing the SDSS-III/BOSS CMASS DR11 data, to control the impact of sky mask and radial selection function. Our solution is based on generating voids from randoms including the same survey geometry and completeness, and a post-processing cleaning procedure in the holes and at the boundaries of the survey. The methodology and optimal selection of void populations validated in this work have been used to perform the first BAO detection from voids in observations, presented in a companion paper.