We analyse the broad-range shape of the monopole and quadrupole correlation functions of the BOSS Data Release 12 ( DR12 ) CMASS and LOWZ galaxy sample to obtain constraints on the Hubble expansion rate H ( z ) , the angular-diameter distance D _ { A } ( z ) , the normalised growth rate f ( z ) \sigma _ { 8 } ( z ) , and the physical matter density \Omega _ { m } h ^ { 2 } .
We adopt wide and flat priors on all model parameters in order to ensure the results are those of a ‘ single-probe ’ galaxy clustering analysis .
We also marginalise over three nuisance terms that account for potential observational systematics affecting the measured monopole .
The Monte Carlo Markov Chain analysis with such wide priors and additional polynomial functions is computationally expensive for advanced theoretical models .
We develop a new methodology to speed up by scanning the parameter space using a fast model first and then applying importance sampling using a slower but more accurate model .

Our measurements for DR12 galaxy sample , using the range 40 h ^ { -1 } Mpc < s < 180 h ^ { -1 } Mpc , are \ { D _ { A } ( z ) r _ { s,fid } / r _ { s } , H ( z ) r _ { s } / r _ { s,fid } , f ( z ) \sigma _ { 8 } ( z ) , \Omega _ { m } h ^ { 2 } \ } = \ { 956 \pm 28 Mpc , 75.0 \pm 4.0 { km } { s } ^ { -1 } { Mpc } ^ { -1 } , 0.397 \pm 0.073 , 0.143 \pm 0.017 \ } at z = 0.32 and \ { 1421 \pm 23 Mpc , 96.7 \pm 2.7 { km } { s } ^ { -1 } { Mpc } ^ { -1 } , 0.497 \pm 0.058 , 0.137 \pm 0.015 \ } at z = 0.59 where r _ { s } is the comoving sound horizon at the drag epoch and r _ { s,fid } = 147.66 Mpc is the sound scale of the fiducial cosmology used in this study .

In addition , we divide each sample ( CMASS and LOWZ ) into two redshift bins ( four bins in total ) to increase the sensitivity of redshift evolution .
However , we do not find improvements in terms of constraining dark energy model parameters .
Combining our measurements with Planck data , we obtain \Omega _ { m } = 0.306 \pm 0.009 , H _ { 0 } = 67.9 \pm 0.7 { km } { s } ^ { -1 } { Mpc } ^ { -1 } , and \sigma _ { 8 } = 0.815 \pm 0.009 assuming \Lambda CDM ; \Omega _ { k } = 0.000 \pm 0.003 assuming oCDM ; w = -1.01 \pm 0.06 assuming w CDM ; and w _ { 0 } = -0.95 \pm 0.22 and w _ { a } = -0.22 \pm 0.63 assuming w _ { 0 } w _ { a } CDM .
Our results show no tension with the flat \Lambda CDM cosmological paradigm .
This paper is part of a set that analyses the final galaxy clustering dataset from BOSS .