Abstract
Metastable states decay at zero temperature through quantum tunnelling at an exponentially small rate, which depends on the Coleman–de Luccia instanton, also known as bounce. In some theories, the bounce may not exist or its on-shell action may be ill-defined or infinite, thus hindering the vacuum decay process. In this paper, we test this possibility in modified theories of gravity interacting with a real scalar field. We consider an Einstein–Hilbert term with a non-minimally coupled scalar field and a quadratic Ricci scalar contribution. To tackle the problem, we use a new analytic method, with which we prove that the scalar field on the bounce has a universal behaviour at large Euclidean radii, almost independently of the potential. Our main result is that the quadratic Ricci scalar prevents the decay, regardless of the other terms in the action.
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