Study of baryon acoustic oscillations with SDSS DR13 data and measurements of ${\Omega }_k$ and ${\Omega }_{\text{DE}}(a)$

Abstract

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 ${\theta }_{\text{MC}}$ of fluctuations of the Cosmic Microwave Background (CMB) we obtain ${\Omega }_k=-0.015\pm 0.030$, ${\Omega }_{\text{DE}}+2.2{\Omega }_k=0.717\pm 0.004$ and $w_1=0.37\pm 0.61$ for dark energy density allowed to vary as ${\Omega }_{\text{DE}}(a)={\Omega }_{\text{DE}}[1+w_1(1-a)]$. We present measurements of ${\Omega }_{\text{DE}}(a)$ 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 ${\Omega }_{\text{DE}}(a)$ constant.

10 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1607.02424, arXiv:1608.08486