Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Euclidean action for vacuum decay in a de Sitter universe   The behavior of the action of the instantons describing vacuum decay in a de
Sitter is investigated. For a near-to-limit instanton (a Coleman-de Luccia
instanton close to some Hawking-Moss instanton) we find approximate formulas
for the Euclidean action by expanding the scalar field and the metric of the
instanton in the powers of the scalar field amplitude. The order of the
magnitude of the correction to the Hawking-Moss action depends on the order of
the instanton (the number of crossings of the barrier by the scalar field): for
instantons of odd and even orders the correction is of the fourth and third
order in the scalar field amplitude, respectively. If a near-to-limit instanton
of the first order exists in a potential with the curvature at the top of the
barrier greater than 4 $\times$ (Hubble constant)$^2$, which is the case if the
fourth derivative of the potential at the top of the barrier is greater than
some negative limit value, the action of the instanton is less than the
Hawking-Moss action and, consequently, the instanton determines the outcome of
the vacuum decay if no other Coleman-de Luccia instanton is admitted by the
potential. A numerical study shows that for the quartic potential the physical
mode of the vacuum decay is given by the Coleman-de Luccia instanton of the
first order also in the region of parameters in which the potential admits two
instantons of the second order.

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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: math
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex