Instanton solutions mediating tunneling between the degenerate vacua in curved space

Abstract

We investigate the instanton solution between the degenerate vacua in curved space. We show that there exist $O(4)$-symmetric solutions not only in de Sitter but also in both flat and anti-de Sitter space. The geometry of the new type of solutions is finite and preserves the $Z_2$ symmetry. The nontrivial solution corresponding to the tunneling is possible only if gravity is taken into account. The numerical solutions as well as the analytic computations using the thin-wall approximation are presented. We expect that these solutions do not have any negative mode as in the instanton solution.

Some typos are corrected and references are added with respect to the published version. 17pages, 11fig

References in corpus (20)

• Thermal derivation of the Coleman-De Luccia tunneling prescription
• Heretics of the False Vacuum: Gravitational Effects On and Of Vacuum Decay 2
• Probabilities in the landscape: The decay of nearly flat space
• Lectures on instantons
• Regulating Eternal Inflation II: The Great Divide
• Hawking-Moss bounces and vacuum decay rates
• The false vacuum bubble nucleation due to a nonminimally coupled scalar field
• Dynamics of false vacuum bubbles: beyond the thin shell approximation
• The number of negative modes of the oscillating bounces
• Dynamical renormalization group methods in theory of eternal inflation
• Gauss-Bonnet Term on Vacuum Decay
• Dynamics of false vacuum bubbles with nonminimal coupling
• The Cosmological Constant Problem and Inflation in the String Landscape
• Domain wall cosmology and multiple accelerations
• Horizons and Tunneling in the Euclidean False Vacuum
• Some Gravitational Instantons
• Domain wall universe in the Einstein-Born-Infeld theory
• Effects of the cosmological expansion on the bubble nucleation rate for relativistic first-order phase transitions
• Eternal inflation and localization on the landscape
• Quantum-classical interactions through the path integral

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• Oscillating instanton solutions in curved space
• Aspects of the negative mode problem in quantum tunneling with gravity
• Coleman-de Luccia instanton in dRGT massive gravity
• Two-loop corrections to false vacuum decay in scalar field theory
• Numerical Analysis of Coleman-de Luccia Tunneling
• Gravitational waves from the vacuum decay with LISA
• The nucleation of false vacuum bubbles with compact geometries
• NNLO corrections to false vacuum decay rate in thin-wall approximation
• Creation of a black hole pair with a domain wall
• Instanton interaction in de Sitter spacetime
• Wormhole Solutions and Pre-inflationary Epoch in $F(R,T)$ Gravity with Axion Fields