The Impossibility of Steady-State Inflation
  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. 
Arvind Borde and Alexander Vilenkin