  When Inflation is embedded in a fundamental theory, such as string theory, it
typically begins when the Universe is already substantially larger than the
fundamental scale [such as the one defined by the string length scale]. This is
naturally explained by postulating a pre-inflationary era, during which the
size of the Universe grew from the fundamental scale to the initial
inflationary scale. The problem then arises of maintaining the [presumed]
initial spatial homogeneity throughout this era, so that, when it terminates,
Inflation is able to begin in its potential-dominated state. Linde has proposed
that a spacetime with compact negatively curved spatial sections can achieve
this, by means of chaotic mixing. Such a compactification will however lead to
a Casimir energy, which can lead to effects that defeat the purpose unless the
coupling to gravity is suppressed. We estimate the value of this coupling
required by the proposal, and use it to show that the pre-inflationary
spacetime is stable, despite the violation of the Null Energy Condition
entailed by the Casimir energy.
