PRIMORDIAL GRAVITATIONAL-WAVES FROM OPEN INFLATION

We calculate the spectrum of gravitational waves generated during infl ation in open (Omega(0)<1) inflationary models. In such models an init ial epoch of old inflation solves the horizon and flatness problems, a nd during this first epoch of inflation the quantum state of the gravi ton field rapidly approaches the Bunch-Davies vacuum. Then the old inf lation ends by the nucleation of a single bubble, inside of which then is a shortened epoch of slow-roll inflation giving Omega(0)<1 today. In this paper we reexpress the Bunch-Davies vacuum for the graviton fi eld in terms of the hyperbolic modes inside the bubble and propagate t hese modes forward in time into the present era. We derive the express ion for the contribution from these gravity waves to the cosmic microw ave background anisotropy including the effect of a finite-energy diff erence across the bubble wall.