  We simulate the evolution of the intergalactic medium (IGM) in a universe
dominated by a cosmological constant. We find that within a few Hubble times
from the present epoch, the baryons will have two primary phases: one phase
composed of low-density, low-temperature, diffuse, ionized gas which cools
exponentially with cosmic time due to adiabatic expansion, and a second phase
of high-density, high-temperature gas in virialized dark matter halos which
cools much more slowly by atomic processes. The mass fraction of gas in halos
converges to ~40% at late times, about twice its calculated value at the
present epoch. We find that in a few Hubble times, the large scale filaments in
the present-day IGM will rarefy and fade away into the low-temperature IGM, and
only islands of virialized gas will maintain their physical structure. We do
not find evidence for fragmentation of the diffuse IGM at later times. More
than 99% of the gas mass will maintain a steady ionization fraction above 80%
within a few Hubble times. The diffuse IGM will get extremely cold and dilute
but remain highly ionized, as its recombination time will dramatically exceed
the age of the universe.
