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.
