  Inflation is known to be generically eternal to the future: the false vacuum
is thermalized in some regions of space, while inflation continues in other
regions. Here, we address the question of whether inflation can also be eternal
to the past. We argue that such a steady-state picture is impossible and,
therefore, that inflation must have had a beginning. First, it is shown that
the old inflationary model is not past-eternal. Next, some necessary conditions
are formulated for inflationary spacetimes to be past-eternal and
future-eternal. It is then shown that these conditions cannot simultaneously
hold in physically reasonable open universes.
