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We present a measurement of the anisotropic void-galaxy cross-correlation function in the CMASS galaxy sample of the BOSS DR12 data release. We perform a joint fit to the data for redshift space distortions (RSD) due to galaxy peculiar velocities and anisotropies due to the Alcock-Paczynski (AP) effect, for the first time using a velocity field reconstruction technique to remove the complicating effects of RSD in the void center positions themselves. Fits to the void-galaxy function give a 1% measurement of the AP parameter combination D₀ (z) H (z) /c=0. 43670. 0045 at redshift z=0. 57, where D₀ is the angular diameter distance and H the Hubble parameter, exceeding the precision obtainable from baryon acoustic oscillations (BAO) by a factor of 3. 5 and free of systematic errors. From voids alone we also obtain a 10% measure of the growth rate, f₈ (z=0. 57) =0. 5010. 051. The parameter degeneracies are orthogonal to those obtained from galaxy clustering. Combining void information with that from BAO and galaxy RSD in the same CMASS sample, we measure D₀ (0. 57) /rₒ=9. 3830. 077 (at 0. 8% precision), H (0. 57) rₒ= (14. 050. 14) 10^3 kms^-1 Mpc^-1 (1%), and f₈=0. 4530. 022 (4. 9%), consistent with cosmic microwave background (CMB) measurements from Planck. These represent a factor 2 improvement in precision over previous results through the inclusion of void information. Fitting a flat cosmological constant model to these results in combination with Planck CMB data, we find up to an 11% reduction in uncertainties on H₀ and ₌ compared to use of the corresponding BOSS consensus values. Constraints on extended models with nonflat geometry and a dark energy of state that differs from w=-1 show an even greater improvement.
Nadathur et al. (Tue,) studied this question.