| Abstract
| - We study the 3D distribution of matter at z∼ 2 using high-resolution spectra of quasi-stellar object (QSO) pairs and simulated spectra drawn from cosmological hydrodynamical simulations. We present a sample of 15 QSOs, corresponding to 21 baselines of angular separations evenly distributed between ∼1 and 14 arcmin, observed with the Ultraviolet and Visual Echelle Spectrograph (UVES) at the European Southern Observatory Very Large Telescope (ESO-VLT). The observed correlation functions of the transmitted flux in the H i Lyman α forest transverse to and along the line of sight are in agreement, implying that the distortions in redshift space due to peculiar velocities are relatively small and - within the relatively large error bars - not significant. The clustering signal is significant up to velocity separations of ∼300 km s−1, corresponding to about 5 h−1 comoving Mpc. Compatibility at the 2σ level has been found both for the autocorrelation and cross-correlation functions and for the set of the cross-correlation coefficients. The analysis focuses in particular on two QSO groups of the sample, the Sextet and the Triplet. Searching for alignments in the redshift space between Lyman α absorption lines belonging to different lines of sight, it has been possible to discover the presence of a wide H i structure extending over about 10 Mpc in comoving space, and give constraints on the sizes of two cosmic underdense regions in the intergalactic medium, which have been detected with a 91 and 86 per cent significance level, respectively, in the Sextet and the Triplet.
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