The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: double-probe measurements from BOSS galaxy clustering \& Planck data -- towards an analysis without informative priors

We develop a new methodology called double-probe analysis with the aim of minimizing informative priors in the estimation of cosmological parameters. We extract the dark-energy-model-independent cosmological constraints from the joint data sets of Baryon Oscillation Spectroscopic Survey (BOSS) galaxy sample and Planck cosmic microwave background (CMB) measurement. We measure the mean values and covariance matrix of $\{R$, $l_a$, ${\mathrm{\Omega }}_b{h}^2$, $n_s$, $log(A_s)$, ${\mathrm{\Omega }}_k$, $H(z)$, $D_A(z)$, $f(z){\sigma }_8(z)\}$, which give an efficient summary of Planck data and 2-point statistics from BOSS galaxy sample, where $R=\sqrt{{\mathrm{\Omega }}_m{H}_0^2}r(z_{\ast })$, and $l_a=\pi r(z_{\ast })\mathrm{/}{r}_s(z_{\ast })$, $z_{\ast }$ is the redshift at the last scattering surface, and $r(z_{\ast })$ and $r_s(z_{\ast })$ denote our comoving distance to $z_{\ast }$ and sound horizon at $z_{\ast }$ respectively. The advantage of this method is that we do not need to put informative priors on the cosmological parameters that galaxy clustering is not able to constrain well, i.e. ${\mathrm{\Omega }}_b{h}^2$ and $n_s$. Using our double-probe results, we obtain ${\mathrm{\Omega }}_m=0.304\pm 0.009$, $H_0=68.2\pm 0.7$, and ${\sigma }_8=0.806\pm 0.014$ assuming $\mathrm{\Lambda }$CDM; and ${\mathrm{\Omega }}_k=0.002\pm 0.003$ and $w=-1.00\pm 0.07$ assuming o$w$CDM. The results show no tension with the flat $\mathrm{\Lambda }$CDM cosmological paradigm. By comparing with the full-likelihood analyses with fixed dark energy models, we demonstrate that the double-probe method provides robust cosmological parameter constraints which can be conveniently used to study dark energy models. We extend our study to measure the sum of neutrino mass and obtain $\mathrm{\Sigma }{m}_{\nu }<0.10\mathrm{/}0.22$ (68%/95%) assuming $\mathrm{\Lambda }$CDM and $\mathrm{\Sigma }{m}_{\nu }<0.26\mathrm{/}0.52$ (68%/95%) assuming $w$CDM. This paper is part of a set that analyses the final galaxy clustering dataset from BOSS.