Study of baryon acoustic oscillations with SDSS DR12 data and measurement of ${\mathrm{\Omega }}_{\text{DE}}(a)$

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 ${\theta }_{\text{MC}}$ of the Cosmic Microwave Background (CMB), we constrain the cosmological parameters in several scenarios. We find $4.3\sigma$ tension between the BAO plus ${\theta }_{\text{MC}}$ data and a cosmology with flat space and constant dark energy density ${\mathrm{\Omega }}_{\text{DE}}(a)$. Releasing one and/or the other of these constraints obtains agreement with the data. We measure ${\mathrm{\Omega }}_{\text{DE}}(a)$ as a function of $a$.