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 centre positions themselves .
Fits to the void-galaxy function give a 1 \% measurement of the AP parameter combination D _ { A } ( z ) H ( z ) / c = 0.4367 \pm 0.0045 at redshift z = 0.57 , where D _ { A } is the angular diameter distance and H the Hubble parameter , exceeding the precision obtainable from baryon acoustic oscillations ( BAO ) by a factor of \sim 3.5 and free of systematic errors .
From voids alone we also obtain a 10 \% measure of the growth rate , f \sigma _ { 8 } ( z = 0.57 ) = 0.501 \pm 0.051 .
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 D _ { A } ( 0.57 ) / r _ { s } = 9.383 \pm 0.077 ( at 0.8 % precision ) , H ( 0.57 ) r _ { s } = ( 14.05 \pm 0.14 ) 10 ^ { 3 } kms ^ { -1 } Mpc ^ { -1 } ( 1 % ) and f \sigma _ { 8 } = 0.453 \pm 0.022 ( 4.9 % ) , consistent with cosmic microwave background ( CMB ) measurements from Planck .
These represent a factor \sim 2 improvement in precision over previous results through the inclusion of void information .
Fitting a flat cosmological constant \Lambda CDM model to these results in combination with Planck CMB data , we find up to an 11 \% reduction in uncertainties on H _ { 0 } and \Omega _ { m } compared to use of the corresponding BOSS consensus values .
Constraints on extended models with non-flat geometry and a dark energy of state that differs from w = -1 show an even greater improvement .