  We introduce in this paper a new framework for obtaining a period of
exponential inflation that is entirely driven by the quadratic kinetic energy
of a scalar field. In contrast to recent attempts to realize scalar field
inflation without potentials (such as k-inflation or ghost inflation), we find
that it is possible to obtain exponential inflation, without invoking any
higher derivative actions, or modifying gravity, and that unlike all previous
approaches, we do not require a $\rho = -p$ phase in order to realize
inflation. The inflaton in our proposed framework is a scalar field with a
quadratic kinetic energy term, but with the `wrong sign'. We take the
perspective that this is due to some temporary instability in our system at
high energies, and provide physical examples of situations where a modulus
field might temprorarily exhibit such behaviour. The deflation of extra
dimensions is a neccesary feature of our framework. However, unlike in previous
attempts at Kaluza-Klein inflation, it is possible to obtain exponential (as
opposed to power law or pole) inflation. We provide several indications of how
one can gracefully exit from this type of inflation.
