On Open Inflation, the string theory landscape and the low CMB quadrupole

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.