False Vacuum In ation with Einstein Gravity

We present a detailed investigation of chaotic in ation models which feature two scalar elds, such that one eld (the in aton) rolls while the other is trapped in a false vacuum state. The false vacuum becomes unstable when the magnitude of the in aton eld falls below some critical value, and a rst or second order transition to the true vacuum ensues. Particular attention is paid to the case, termed `Hybrid In ation' by Linde, where the false vacuum energy density dominates, so that the phase transition signals the end of in ation. We focus mostly on the case of a second order transition, but treat also the rst order case and discuss bubble production in that context for the rst time. False vacuum dominated in ation is dramatically di erent from the usual true vacuum case, both in its cosmology and in its relation to particle physics. The spectral index of the adiabatic density perturbation originating during in ation can be indistinguishable from 1, or it can be up to ten percent or so higher. The energy scale at the end of in ation can be anywhere between 1016 GeV, which is familiar from the true vacuum case, and 1011 GeV. On the other hand reheating is prompt, so the reheat temperature cannot be far below 10 GeV. Cosmic strings or other topological defects are almost inevitably produced at the end of in ation, and if the in ationary energy scale is near its upper limit they contribute signi cantly to large scale structure formation and the cosmic microwave background anisotropy. Turning to the particle physics, false vacuum in ation occurs with the in aton eld far below the Planck scale and is therefore somewhat easier to implement in the context of supergravity than true vacuum chaotic in ation. The smallness of the in aton mass compared with the in ationary Hubble parameter still presents a di culty for generic supergravity theories. Remarkably however, the di culty can be avoided in a natural way for a class of supergravity models that follow from orbifold compacti cation of superstrings. This opens up the prospect of a truly realistic, superstring derived theory of in ation. One possibility, which we show to be viable at least in the context of global supersymmetry, is that the Peccei-Quinn symmetry is responsible for the false vacuum. PACS numbers: 98.80.Cq, 04.50.+h