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.
