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.Comment: 16 pages, 3 figures, references adde

No abstract

The false vacuum decay in a brane world model is studied in this work. We investigate the vacuum decay via the Coleman-de Luccia instanton, derive explicit approximative expressions for the Coleman-de Luccia instanton which is close to a Hawking-Moss instanton and compare the results with those already obtained within Einstein's theory of relativity.

In this paper, a six‐dimensional model of flexible prices with the monetary and fiscal policy mix, describing the development of the firms’ private debt, the output, the expected rate of inflation, the rate of interest, government expenditure, and government bonds are analyzed. The stress put on the “twin debt accumulation” means that in our model both private debt accumulation and the public debt (government bond) accumulation are explicitly introduced. Questions concerning the existence of limit cycles around its normal equilibrium point are investigated. The bifurcation equation is found. The formulae for the calculation of its coefficients are gained. Numerical example illustrating the results attained is presented by means of numerical simulations.

No abstract