We study the kinematics of the gaseous cosmic web at high redshift using Lyα forest absorption in multiple QSO sight lines. Observations of the projected velocity shifts between Lyα absorbers common to the lines of sight to a gravitationally lensed QSO and three more widely separated QSO pairs are used to directly measure the expansion of the cosmic web in units of the Hubble velocity, as a function of redshift and spatial scale. The lines of sight used span a redshift range from about 2 to 4.5 and represent transverse scales from the subkiloparsec range to about 300 h physical kpc. Using a simple analytic model and a cosmological hydrodynamic simulation, we constrain the underlying three-dimensional distribution of expansion velocities from the observed line-of-sight distribution of velocity shear across the plane of the sky. The shape of the shear distribution and its width (14.9 km s^-1 rms for a physical transverse separation of 61 h kpc at z = 2, 30.0 km s^-1 for 261 h kpc at z = 3.6) are found to be in good agreement with the IGM undergoing large-scale motions dominated by the Hubble flow, making this one of the most direct observations possible of the expansion of the universe. However, modeling the Lyα clouds with a simple "expanding pancake" model, the average expansion velocity of the gaseous structures causing the Lyα forest in the lower redshift (z ~ 2) smaller separation (61 kpc) sample appears about 20% lower than the local Hubble expansion velocity.

In order to understand the observed velocity distribution further we investigated the statistical distribution of expansion velocities in cosmological Lyα forest simulations. The mean expansion velocity in the (z ~ 2, separation ~ 60 kpc) simulation is indeed somewhat smaller than the Hubble velocity, as found in the real data. We interpret this finding as tentative evidence for some Lyα forest clouds breaking away from the Hubble flow and undergoing the early stages of gravitational collapse. However, the distribution of velocities is highly skewed, and the majority of Lyα forest clouds at all redshifts from 2 to 3.8 expand with super-Hubble velocities, typically about 5%-20% faster than the Hubble flow. This behavior is explained if most Lyα forest clouds in the column density range typically detectable are expanding filaments that stretch and drain into more massive nodes. The significant difference seen in the velocity distributions between the high- and low-redshift samples may conceivably reflect actual peculiar deceleration, the differences in spatial scale, or our selecting higher densities at lower redshift for a given detection threshold for Lyα forest lines.

We also investigate the alternative possibility that the velocity structure of the general Lyα forest could have an entirely different, local origin, as expected if the Lyα forest were produced or at least significantly modified by galactic feedback, e.g., winds from star-forming galaxies at high redshift. However, we find no evidence that the observed distribution of velocity shear is significantly influenced by processes other than Hubble expansion and gravitational instability. To avoid overly disturbing the IGM, galactic winds may be old and/or limp by the time we observe them in the Lyα forest, or they may occupy only an insignificant volume fraction of the IGM. We briefly discuss the observational evidence usually presented in favor of an IGM afflicted by high-redshift extragalactic superwinds and find much of it ambiguous. During the hierarchical buildup of structure, galaxies are expected to spill parts of their interstellar medium and to heat and stir the IGM in ways that make it hard to disentangle this gravitational process from the effects of winds.