Search for a direction in the forest of Lyman-$\alpha$

We report the first test of isotropy of the Universe in the matter dominated epoch using the Lyman-$\alpha$ forest data from the high redshift quasars ($z>2$) from SDSS-III BOSS-DR9 datasets. Using some specified data cuts, we obtain the probability distribution function (PDF) of the Lyman-$\alpha$ forest transmitted flux and use the statistical moments of the PDF to address the isotropy of the Universe. In an isotropic Universe one would expect the transmitted flux to have consistent statistical characteristics in different parts of the sky. We trisect the total survey area of 3275 ${\rm deg}^2$ along the galactic latitude and using quadrant convention. We also make three subdivisions in the data for three different signal-to-noise-ratios (SNR). Finally we obtain and compare the statistical moments in the mean redshifts of 2.3, 2.6 and 2.9. We find, that the moments from all patches agree at all redshifts and at all SNRs, within 3$\sigma$ uncertainties. Since Lyman-$\alpha$ transmitted flux directly maps the neutral hydrogen distribution in the inter galactic medium (IGM), our results indicate, within the limited survey area and sensitivity of the data, the distribution of the neutral hydrogen in the Universe is consistent with isotropic distribution. We should mention that we report few deviations from isotropy in the data with low statistical significance. Increase in survey area and larger amount of data are needed to make any strong conclusion about these deviations.
Comment: 16 pages, 5 figures, 2 tables