Study of baryon acoustic oscillations with SDSS DR12 data and measurements of ${\mathrm{\Omega }}_k$ and ${\mathrm{\Omega }}_{\text{DE}}(a)$. 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 $d_{\text{BAO}}$ 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 ${\theta }_{\text{MC}}$ of the Cosmic Microwave Background (CMB), we constrain the curvature parameter ${\mathrm{\Omega }}_k$ and the dark energy density ${\mathrm{\Omega }}_{\text{DE}}(a)$ as a function of the expansion parameter $a$ in several scenarios. These observables are further constrained with external measurements of $h$ and ${\mathrm{\Omega }}_{\text{b}}{h}^2$. We find some tension between the data and a cosmology with flat space and constant dark energy density ${\mathrm{\Omega }}_{\text{DE}}(a)$.