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

Abstract: 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 $a$.