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 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 .