Because space is expanding at an exponential rate during inflation, this means that exponentially more regions of space are being created as time goes on. In a few regions, inflation will come to an end: where the field rolls down into the valley. But in others, inflation will continue on, giving rise to more and more space surrounding each and every region where inflation ends. The rate of inflation is far more rapid than even the maximum rate of expansion of a matter-and-energy-filled Universe, so in very short order, the inflating parts take over everything. According to the viable mechanisms that give us enough inflation to produce the Universe we see, there are many more regions of space surrounding our own — where inflation did end — where inflation doesn’t end right away.