Study of baryon acoustic oscillations with SDSS DR12 data and measurements of $Omega_k$ and $Omega_textrm{DE}(a)$. Part II

We define Baryon Acoustic Oscillation (BAO) observables $hat{d}_alpha(z, z_c)$, $hat{d}_z(z, z_c)$, and $hat{d}_/(z, z_c)$ that do not depend on any cosmological parameter. From each of these observables we recover the BAO correlation length $d_textrm{BAO}$ with its respective dependence on cosmological parameters. These BAO observables are measured as a function of redshift $z$ with the Sloan Digital Sky Survey (SDSS) data release DR12. From the BAO measurements alone, or together with the correlation angle $theta_textrm{MC}$ of the Cosmic Microwave Background (CMB), we constrain the curvature parameter $Omega_k$ and the dark energy density $Omega_textrm{DE}(a)$ as a function of the expansion parameter $a$ in several scenarios. These observables are further constrained with external measurements of $h$ and $Omega_textrm{b} h^2$. We find some tension between the data and a cosmology with flat space and constant dark energy density $Omega_textrm{DE}(a)$.