The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Towards a computationally efficient analysis without informative priors

We develop a new computationally efficient methodology called double-probe analysis with the aim of minimizing informative priors (those coming from extra probes) in the estimation of cosmological parameters. Using our new methodology, we extract the dark energy model-independent cosmological constraints from the joint data sets of the Baryon Oscillation Spectroscopic Survey (BOSS) galaxy sample and Planck cosmic microwave background (CMB) measurements. We measure the mean values and covariance matrix of {R, l_a, Ω_bh², n_s, log(A_s), Ω_k, H(z), D_A(z), f(z)σ₈(z)}, which give an efficient summary of the Planck data and two-point statistics from the BOSS galaxy sample. The CMB shift parameters are R=ΩmH20√r(z∗) and l_a = πr(z_*)/r_s(z_*), where z_* is the redshift at the last scattering surface, and r(z_*) and r_s(z_*) denote our comoving distance to the z_* and sound horizon at z_*, respectively; Ω_b is the baryon fraction at z = 0. This approximate methodology guarantees that we will not need to put informative priors on the cosmological parameters that galaxy clustering is unable to constrain, i.e. Ω_bh² and n_s. The main advantage is that the computational time required for extracting these parameters is decreased by a factor of 60 with respect to exact full-likelihood analyses. The results obtained show no tension with the flat Λ cold dark matter (ΛCDM) cosmological paradigm. By comparing with the full-likelihood exact analysis with fixed dark energy models, on one hand we demonstrate that the double-probe method provides robust cosmological parameter constraints that can be conveniently used to study dark energy models, and on the other hand we provide a reliable set of measurements assuming dark energy models to be used, for example, in distance estimations. We extend our study to measure the sum of the neutrino mass using different methodologies, including double-probe analysis (introduced in this study), full-likelihood analysis and single-probe analysis. From full-likelihood analysis, we obtain Σm_ν < 0.12 (68 per cent), assuming ΛCDM and Σm_ν < 0.20 (68 per cent) assuming owCDM. We also find that there is degeneracy between observational systematics and neutrino masses, which suggests that one should take great care when estimating these parameters in the case of not having control over the systematics of a given sample.