False Vacuum Inflation with Einstein Gravity

TL;DR

Copeland, Liddle, Lyth, Stewart, and Wands analyze false vacuum inflation within Einstein gravity using a two-field hybrid framework where inflation proceeds with ψ in a false vacuum and ends via a second-field instability or a slow-roll exit. They derive the inflationary dynamics, COBE normalization, and the resulting spectra, showing that false vacuum domination can yield a nearly scale-invariant or slightly blue-tilted spectrum (n ≈ 1 up to ≈ 1.14) with negligible tensor modes in typical regimes. The work explores second-order and first-order phase-transition endings, examines defect production at the end of inflation (strings, monopoles, textures), and discusses realistic particle-physics realizations including simple SUSY models, supergravity, and string-inspired constructions that can naturally suppress dangerous Hubble-scale masses. The findings illuminate rich phenomenology and potential observational signatures while outlining constraints from defect formation and big-bubble nucleation, establishing false vacuum hybrid inflation as a viable alternative with connections to high-energy theories.

Abstract

We investigate chaotic inflation models with two scalar fields, such that one field (the inflaton) rolls while the other is trapped in a false vacuum state. The false vacuum becomes unstable when the inflaton field falls below some critical value, and a first or second order transition to the true vacuum ensues. Particular attention is paid to Linde's second-order `Hybrid Inflation'; with the false vacuum dominating, inflation differs 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 can be very close to 1, or it can be around ten percent higher. The energy scale at the end of inflation can be anywhere between $10^{16}$\,GeV and $10^{11}$\,GeV, though reheating is prompt so the reheat temperature can't be far below $10^{11}\,$GeV. Topological defects are almost inevitably produced at the end of inflation, and if the inflationary energy scale is near its upper limit they can have significant effects. Because false vacuum inflation occurs with the inflaton field far below the Planck scale, it is easier to implement in the context of supergravity than standard chaotic inflation. That the inflaton mass is small compared with the inflationary Hubble parameter is still a problem for generic supergravity theories, but remarkably this can be avoided in a natural way for a class of supergravity models which follow from orbifold compactification of superstrings. This opens up the prospect of a truly realistic, superstring