Abstract
We develop the formalism for computing gravitational corrections to vacuum decay from de Sitter space as a sub-Planckian perturbative expansion. Non-minimal coupling to gravity can be encoded in an effective potential. The Coleman bounce continuously deforms into the Hawking-Moss bounce, until they coincide for a critical value of the Hubble constant. As an application, we reconsider the decay of the electroweak Higgs vacuum during inflation. Our vacuum decay computation reproduces and improves bounds on the maximal inflationary Hubble scale previously computed through statistical techniques.
Highlights
At the critical value H = Hcr where Coleman and Hawking-Moss solutions merge, vacuum decay is suppressed by large actions SHM = 4π2/3b ≈ 13000, and the coefficient ∆ that determines the behaviour of Coleman solutions is positive, such that Coleman bounces exist for H > Hcr and are irrelevant in view of SColeman > SHM
The bounce action is obtained as a power series in 1/MPl, and a non-minimal scalar coupling to gravity can be reabsorbed in an effective scalar potential, see eq (2.19)
We found that, increasing H, the flat-space Coleman bounce continuously deforms into the Hawking-Moss bounce
Summary
Coleman and de Luccia [2] developed the formalism for computing vacuum decay from a de Sitter space with Hubble constant H taking gravity into account. We review this formalism, extend it to a general non-minimal coupling of the Higgs to gravity and derive simplified expressions that hold in the sub-Planckian limit H, M MPl, where M is the mass scale that characterises the scalar potential and thereby the bounce. In the semiclassical (small ) limit the decay rate Γ of the false vacuum per unit of space-time volume V is given by [1, 2, 26, 27]. In a nontrivial (r-dependent) bounce h(r) does not tend to the false vacuum solution, hfalse = 0, as r → rmax, unless we are in the flat space case, rmax → ∞.2. For rmax < ∞, the only regular function that goes indefinitely close to the false vacuum solution as r → rmax is the false vacuum solution itself
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