We report a detection of the baryon acoustic oscillation ( BAO ) feature in the flux-correlation function of the Ly \alpha forest of high-redshift quasars with a statistical significance of five standard deviations .
The study uses 137,562 quasars in the redshift range 2.1 \leq z \leq 3.5 from the Data Release 11 ( DR11 ) of the Baryon Oscillation Spectroscopic Survey ( BOSS ) of SDSS-III .
This sample contains three times the number of quasars used in previous studies .
The measured position of the BAO peak determines the angular distance , D _ { A } ( z = 2.34 ) and expansion rate , H ( z = 2.34 ) , both on a scale set by the sound horizon at the drag epoch , r _ { d } .
We find D _ { A } / r _ { d } = 11.28 \pm 0.65 ( 1 \sigma ) ^ { +2.8 } _ { -1.2 } ( 2 \sigma ) and D _ { H } / r _ { d } = 9.18 \pm 0.28 ( 1 \sigma ) \pm 0.6 ( 2 \sigma ) where D _ { H } = c / H .
The optimal combination , \sim D _ { H } ^ { 0.7 } D _ { A } ^ { 0.3 } / r _ { d } is determined with a precision of \sim 2 \% .
For the value r _ { d } = 147.4 ~ { } { Mpc } , consistent with the cosmic microwave background power spectrum measured by Planck , we find D _ { A } ( z = 2.34 ) = 1662 \pm 96 ( 1 \sigma ) ~ { } { Mpc } and H ( z = 2.34 ) = 222 \pm 7 ( 1 \sigma ) ~ { } { km s ^ { -1 } Mpc ^ { -1 } } .
Tests with mock catalogs and variations of our analysis procedure have revealed no systematic uncertainties comparable to our statistical errors .
Our results agree with the previously reported BAO measurement at the same redshift using the quasar-Ly \alpha forest cross-correlation .
The autocorrelation and cross-correlation approaches are complementary because of the quite different impact of redshift-space distortion on the two measurements .
The combined constraints from the two correlation functions imply values of D _ { A } / r _ { d } that are 7 % lower and 7 % higher for D _ { H } / r _ { d } than the predictions of a flat \Lambda CDM cosmological model with the best-fit Planck parameters .
With our estimated statistical errors , the significance of this discrepancy is \approx 2.5 \sigma .