Study of baryon acoustic oscillations with SDSS DR13 data and measurements of $Omega_k$ and $Omega_textrm{DE}(a)$

We measure the baryon acoustic oscillation (BAO) observables $hat{d}_alpha(z, z_c)$, $hat{d}_z(z, z_c)$, and $hat{d}_/(z, z_c)$ as a function of redshift $z$ in the range 0.1 to 0.7 with Sloan Digital Sky Survey (SDSS) data release DR13. These observables are independent and satisfy a consistency relation that provides discrimination against miss-fits due to background fluctuations. From these measurements and the correlation angle $theta_textrm{MC}$ of fluctuations of the Cosmic Microwave Background (CMB) we obtain $Omega_k = -0.015 pm 0.030$, $Omega_{textrm{DE}} + 2.2 Omega_k = 0.717 pm 0.004$ and $w_1 = 0.37 pm 0.61$ for dark energy density allowed to vary as $Omega_{textrm{DE}}(a) = Omega_{textrm{DE}} [ 1 + w_1 ( 1 - a)]$. We present measurements of $Omega_{textrm{DE}}(a)$ at six values of the expansion parameter $a$. Fits with several scenarios and data sets are presented. The data is consistent with space curvature parameter $Omega_k = 0$ and $Omega_{textrm{DE}}(a)$ constant.