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تسجيل مستخدم جديدColeman-de Luccia Tunneling Wave Function
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We revisit the famous Coleman-de Luccia formalism for decay of false vacuum in gravitational theory. Since the corresponding wave function is time-independent we argue that its instantons interpretation as the decay rate probability is problematic. We instead propose that such phenomenon can better be described by the Wheeler-de Witts wave function. To do so, the Hamilton-Jacobi formalism is employed in the WKB approximation. The scalar and gravitational fields can then be treated as a two-dimensional effective metric. For a particular case of dS-to-dS tunneling, we calculated the wave function and found that it depends only on the potential of the false, and not on the true, vacuum; reminiscent of, though in totally different formalism with, the Hawking-Moss result. In general, this alternative approach might have significant impact on the study of very early universe and quantum cosmology.
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We study Coleman-de Luccia tunneling in some detail. We show that, for a single scalar field potential with a true and a false vacuum, there are four types of tunneling, depending on the properties of the potential. A general tunneling process involv
es a combination of thermal (Gibbons-Hawking temperature) fluctuation part way up the barrier followed by quantum tunneling. The thin-wall approximation is a special limit of the case (of only quantum tunneling) where inside the nucleation bubble is the true vacuum while the outside reaches the false vacuum. Hawking-Moss tunneling is the (only thermal fluctuation) limit of the case where the inside of the bubble does not reach the true vacuum at the moment of its creation, and the outside is cut off by the de Sitter horizon before it reaches the false vacuum. We estimate the corrections to the Hawking-Moss formula, which can be large. In all cases, we see that the bounce of the Euclidean action decreases rapidly as the vacuum energy density increases, signaling that the tunneling is not exponentially suppressed. In some sense, this phenomenon may be interpreted as a finite temperature effect due to the Gibbons-Hawking temperature of the de Sitter space. As an application, we discuss the implication of this tunneling property to the cosmic landscape.
The usual (type A) thin-wall Coleman-de Luccia instanton is made by a bigger-than-half sphere of the false vacuum and a smaller-than-half sphere of the true vacuum. It has a the standard O(4) symmetric negative mode associated with changing the size
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