  Observations from the HUT and the HST have recently detected HeII absorption
along the lines of sight to two high redshift quasars. We use cosmological
simulations with gas dynamics to investigate HeII absorption in the cold dark
matter (CDM) theory of structure formation. We consider two Omega=1 CDM models
with different normalizations and one Omega_0=0.4 CDM model, all incorporating
the photoionizing UV background spectrum computed by Haardt & Madau (1996). The
simulated gas distribution, combined with the H&M spectral shape, accounts for
the relative observed values of taubar_HI and taubar_HeII, the effective mean
optical depths for HI and HeII absorption. If the background intensity is as
high as H&M predict, then matching the absolute values of taubar_HI and
taubar_HeII requires a baryon abundance larger (by factors between 1.5 and 3
for the various CDM models) than our assumed value of Omega_b h^2=0.0125. The
simulations reproduce the evolution of taubar_heII over the observed redshift
range, 2.2 < z < 3.3, if the HeII photoionization rate remains roughly
constant. HeII absorption in the CDM simulations is produced by a diffuse,
fluctuating, intergalactic medium, which also gives rise to the HI ly-alpha
forest. Much of the HeII opacity arises in underdense regions where the HI
optical depth is very low. We compute statistical properties of the HeII and HI
absorption that can be used to test the CDM models and distinguish them from an
alternative scenario in which the HeII absorption is caused by discrete,
compact clouds. The CDM scenario predicts that a substantial amount of baryonic
material resides in underdense regions at high redshift. HeII absorption is the
only sensitive probe of such extremely diffuse, intergalactic gas, so it can
provide a vital test of this fundamental prediction.
