Oscillating Instantons as Homogeneous Tunneling Channels

Physical Review Letters, 1993

Gravitational instantons, solutions to the euclidean Einstein equations, with topology R 3 XS 1 arise naturally in any discussion of finite temperature quantum gravity. This Letter shows that all such instantons (irrespective of their interior behaviour) must have the same asymptotic structure as the Schwarzschild instanton.

Physical Review D, 2010

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.

Journal of High Energy Physics, 2015

We study homogeneous gravitational instantons, conventionally called the Hawking-Moss (HM) instantons, in bigravity theory. The HM instantons describe the amplitude of quantum tunneling from a false vacuum to the true vacuum. Corrections to General Relativity (GR) are found in a closed form. Using the result, we discuss the following two issues: reduction to the de Rham-Gabadadze-Tolley (dRGT) massive gravity and the possibility of preference for a large e-folding number in the context of the Hartle-Hawking (HH) no-boundary proposal. In particular, concerning the dRGT limit, it is found that the tunneling through the so-called self-accelerating branch is exponentially suppressed relative to the normal branch, and the probability becomes zero in the dRGT limit. As far as HM instantons are concerned, this could imply that the reduction from bigravity to the dRGT massive gravity is ill-defined.

Phys Rev Lett, 1992

Gravitational instantons, solutions to the euclidean Einstein equations, with topology $R^3 XS^1$ arise naturally in any discussion of finite temperature quantum gravity. This Letter shows that all such instantons (irrespective of their interior behaviour) must have the same asymptotic structure as the Schwarzschild instanton. Using this, it can be shown that if the Ricci tensor of the manifold is non-negative it must be flat. One special case is when the Ricci tensor vanishes; hence one can conclude that there is no nontrivial vacuum gravitational instanton. This result has uses both in quantum and classical gravity. It places a significant restriction on the instabilities of hot flat space. It also can be used to show that any static vacuum Lorentzian Kaluza-Klein solution is flat.

Nuclear Physics B, 1978

Gravitational instantons are complete non-singular positive definite metrics satisfying the Einstein equations with or without cosmological constant. We treat quantum fluctuations about such solutions and introduce a useful decomposition of the space of gravitational degrees of freedom in terms of which the one-loop corrections take an especially simple form. We treat in detail the question of zero modes, and the fluctuations about de Sitter space.

Nuclear Physics B, 2002

Instanton and wormhole solutions are constructed in a d-dimensional gravity theory with an axion-dilaton pair of scalar fields. We discuss the cases of vanishing, positive and negative cosmological constant. *

Physical review, 1988

New Euclidean solutions, describing the nucleation of a baby universe, are presented for an axion (described by an antisymmetric tensor field strength of rank D -1 in D dimensions) coupled to grav- ity including a cosmological constant. It has long been speculated that the geometry of space-time should fluctuate at distances of the Planck scale. This possibility that quantum gravity allow fluc- tuations in topology has recently been receiving serious consideration by many authors. The work of Gid- dings and Strominger is based on a definite axionic in- stanton. The four-dimensional Euclidean solution in- volves an axion (given as a three-form field strength) cou- pled to Einstein gravity, and describes the nucleation of a baby universe, which carries ofl' a definite axion charge. In the present paper, we briefly report two extensions of this solution. The first is the inclusion of @ cosmological constant. The resulting instanton may be used to de- scribe tunneling between a large de Sitter space and a Planckian Robertson-Walker universe. The second ex- tension is finding analogous solutions for space-time di- mensions other than four. This requires replacing the rank-three antisymmetric tensor field strength by one of rank D -1 in D dimensions. Such higher-rank tensor fields arise in higher-dimensional supergravity theories.

Journal of High Energy Physics, 2022

We present novel regular Euclidean solutions to General Relativity in presence of Maxwell and conformally coupled scalar fields. In particular, we consider metrics of the Eguchi-Hanson and Taub-NUT families to solve the field equations analytically. The solutions have nontrivial topology labeled by the Hirzebruch signature and Euler characteristic that we compute explicitly. We find that, although the solutions are locally inequivalent with the original (anti-)self-dual Eguchi-Hanson metric, they have the same global properties in the flat limit. We revisit the Taub-NUT solution previously found in the literature, analyze their nuts and bolts structure, and obtain the renormalized Euclidean on-shell action as well as their topological invariants. Additionally, we discuss how the solutions get modified in presence of higher-curvature corrections that respect conformal invariance. In the conformally invariant case, we obtain novel Eguchi-Hanson and Taub-NUT solutions and demonstrate that both Euclidean on-shell action and Noether-Wald charges are finite without any reference to intrinsic boundary counterterms.

2009

All known gravitational instantons with Λ > 0 (S 4 , CP 2 , S 2 ×S 2 and CP #CP 2) are described. They are all special cases of the Taub-NUT-Λ local solution. Hence they are Type D and are locally conformably Kähler. They all may be expressed in Bianchi IX form and have four or more Killing vectors. * This is a paper I presented at a conference in Moscow in December 1978, but it was never published. Hari K. Kunduri kindly typed it up for those interested in its description of the four-dimensional gravitational instantons with positive cosmological constant known in 1978.

Physics Letters B, 2016

In this paper, we investigate various types of Fubini instantons in the Dilatonic Einstein-Gauss-Bonnet theory of gravitation which describes the decay of the vacuum state at a hilltop potential through tunneling without barrier. It is shown that the vacuum states are modified by the non-minimally coupled higher-curvature term. Accordingly, we present the new solutions which describe the tunneling from new vacuum states in anti-de Sitter and de Sitter backgrounds. The decay probabilities of the vacuum states are also influenced. We thus show that the semiclassical exponents can be decreased for specific parameter ranges, thereby increasing tunneling probability.