Gravity Waves from Instantons.pdf

a r X i v : a s t r o - p h / 9 9 0 3 0 7 5 v 1 3 M a r 1 9 9 9 Gravity Waves from Instantons Thomas Hertog?? and Neil Turok? DAMTP, Silver St, Cambridge, CB3 9EW, U.K. (February 1, 2008) Abstract We perform a first principles computation of the spectrum of gravity waves produced in open inflationary universes. The background spacetime is taken to be the continuation of an instanton saddle point of the Euclidean no bound- ary path integral. The two-point tensor correlator is computed directly from the path integral and is shown to be unique and well behaved in the in- frared. We discuss the tensor contribution to the cosmic microwave back- ground anisotropy and show how it may provide an observational discriminant between different types of primordial instantons. I. INTRODUCTION The inflationary universe scenario provides an appealing explanation for the smoothness and flatness of the present universe, as well as a mechanism for the origin of density fluc- tuations. Until recently it was believed that inflation inevitably predicted a flat ?0 = 1 universe. However in [1] it was shown that with mild fine tuning an open universe is also possible. The potential must have a sharp false vacuum in which the field is assumed to have become trapped. The field is then assumed to tunnel out via an instanton known as the Coleman-De Luccia instanton [2], producing a bubble within which slow roll inflation occurs. The interior of the bubble produced via the Coleman-De Luccia instanton is an infinite inflating open universe. Such models provide important counter-examples to the standard folklore but require quite contrived scalar field potentials. Recently, however, Hawking and one of us showed that open inflation can occur much more generally. We found a new class of instantons [3] that exist for essentially any inflationary potential, and provide saddle points of the Euclidean path integral. The continuation of these instantons is similar to that of the Coleman- De Luccia i