Study of baryon acoustic oscillations with SDSS DR12 data and measurement of $Omega_textrm{DE}(a)$

We define Baryon Acoustic Oscillation (BAO) distances $hat{d}_alpha(z, z_c)$, $hat{d}_z(z, z_c)$, and $hat{d}_/(z, z_c)$ that do not depend on cosmological parameters. These BAO distances are measured as a function of redshift $z$ with the Sloan Digital Sky Survey (SDSS) data release DR12. From these BAO distances alone, or together with the correlation angle $theta_textrm{MC}$ of the Cosmic Microwave Background (CMB), we constrain the cosmological parameters in several scenarios. We find $4.3 sigma$ tension between the BAO plus $theta_textrm{MC}$ data and a cosmology with flat space and constant dark energy density $Omega_textrm{DE}(a)$. Releasing one and/or the other of these constraints obtains agreement with the data. We measure $Omega_textrm{DE}(a)$ as a function of $a$.