How stable is our vacuum?

Abstract

It is possible that the vacuum state we live in is not the absolute lowest one. In many spontaneously broken field theories a local minimum of the effective potential, which can be quite stable, can exist for certain parameter values. The Universe, starting at a high temperature, might have supercooled in such a local minimum. If such a metastable minimum is separated by a high enough barrier from the absolute minimum, the tunneling rate from the ‘false’ to the ‘true’ vacuum may be slow enough to not have occurred in one Hubble-spacetime-volume^1,2. In that case our vaccum state might suddenly disappear if a bubble of real vacuum formed which was large enough for the bulk energy gain (equal to the product of the volume and the potential drop between false and true vacua) to exceed the surface energy density in its walls (proportional to the barrier potential). Such a bubble would expand at close to the speed of light, with enormous energy release, leaving a large attractive (ρ = −p < 0) cosmological constant in the interior, with a geometry close to anti-deSitter space¹. This space-time is singularity-free if a strict vacuum, but any non-zero particle density would cause singularities to develop quickly. Although the persistence of our present vacuum for 10¹⁰ yr implies that a spontaneous transition via tunnelling is unlikely, we can ask whether a new generation of elementary particle accelerators might trigger such an unfortunate event. We show here that this chance, fortunately, is completely negligible since the region inside our past light cone has already survived some 10⁵ cosmic ray collisions at centre of mass energies of 10¹¹ GeV and higher.