We measure the baryon acoustic oscillation (BAO) observables , , and as a function of red shift 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 of fluctuations of the Cosmic Microwave Background (CMB), we obtain , and for dark energy density allowed to vary as . We present measurements of 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？ and constant.
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, ![\"\"](\"Edit_05133e35-04fc-4899-a651-084ad8e2818d.bmp\")
, and![\"\"](\"Edit_fd3eec2c-552e-4b84-89c5-6c68eacf1445.bmp\")
as a function of red shift 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 ![\"\"](\"Edit_57c9842b-bc36-4092-917e-f08e26e2e27d.bmp\")
of fluctuations of the Cosmic Microwave Background (CMB), we obtain ![\"\"](\"Edit_0426d546-d663-4b94-86cd-e97a1d52206c.bmp\")
, ![\"\"](\"Edit_9e018ed4-779e-457f-9ba8-89fd99bcb7c1.bmp\")
and ![\"\"](\"Edit_417bceba-559a-44ca-99aa-3ce94d7bcf64.bmp\")
for dark energy density allowed to vary as ![\"\"](\"Edit_222e6d3d-8bc3-40bf-bc00-b26c9189d1ad.bmp\")
. We present measurements of ![\"\"](\"Edit_5112fe1f-f91a-42f5-9ede-74c54c7be82f.bmp\")
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？![\"\"](\"Edit_a95e14d6-2b11-4b16-8bb5-3e46503db842.bmp\")
and ![\"\"](\"Edit_38f2fcbe-5ab3-4214-bfbf-a7243dba5d12.bmp\")
constant.
