  Cosmologists have embraced a particular ad hoc formula for the primordial
power spectrum from inflation for universes with $\Omega_0 < 1$. However, the
so-called ``Open Inflation'' models, which are attracting renewed interest in
the context of the ``string theory landscape'' give a different result, and
offer a more fully developed picture of the cosmology and fundamental physics
basis for inflation with $\Omega_0 < 1$. The Open Inflation power spectrum
depends not only on $\Omega_0$, but on the parameters of the effective fields
that drive the universe {\em before} the Big Bang (in ``another part of the
landscape''). This paper considers the search for features in CMB temperature
anisotropy data that might reflect a primordial spectrum of the Open Inflation
form. We ask whether this search could teach us about high energy physics that
described the universe before the onset of the Big Bang, and perhaps even
account for the low CMB quadrupole. Unfortunately our conclusion is that the
specific features we consider are unobservable even with future experiments
although we note a possible loophole connected with our use of the thin wall
approximation.
