Oscillating Fubini instantons in curved space

International Journal of Modern Physics A, 2013

In this paper, we study Einstein gravity with a minimally coupled scalar field accompanied with a potential, assuming an O(4) symmetric metric ansatz. We call an Euclidean instanton is to be an oscillating instanton, if there exists a point where the derivative of the scale factor and the scalar field vanish at the same time. Then, we can prove that the oscillating instanton can be analytically continued, both as inhomogeneous and homogeneous tunneling channels. Here, we especially focus on the possibility of a homogeneous tunneling channel. For the existence of such an instanton, we have to assume three things: (1) there should be a local maximum and the curvature of the maximum should be sufficiently large, (2) there should be a local minimum and (3) the other side of the potential should have a sufficiently deeper vacuum. Then, we can show that there exists a number of oscillating instanton solutions and their probabilities are higher compared to the Hawking–Moss instantons. We a...

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.

Physical review, 1994

The tunneling rates for scalar fields with quartic potentials in de Sitter space in the limit of no gravitational back reaction are calculated numerically and the results are fitted by analytic formulae.

Journal of Cosmology and Astroparticle Physics, 2013

As a first step toward understanding a lanscape of vacua in a theory of non-linear massive gravity, we consider a landscape of a single scalar field and study tunneling between a pair of adjacent vacua. We study the Hawking-Moss (HM) instanton that sits at a local maximum of the potential, and evaluate the dependence of the tunneling rate on the parameters of the theory. It is found that provided with the same physical HM Hubble parameter HHM , depending on the values of parameters α3 and α4 in the action (2.2), the corresponding tunneling rate can be either enhanced or suppressed when compared to the one in the context of General Relativity (GR). Furthermore, we find the constraint on the ratio of the physical Hubble parameter to the fiducial one, which constrains the form of potential. This result is in sharp contrast to GR where there is no bound on the minimum value of the potential.

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.

JCAP 1703 (2017) no.03, 044, 2017

In this work, we investigate O(4)-symmetric instantons within the Eddington-inspired-Born-Infeld gravity theory (EiBI) . We discuss the regular Hawking-Moss instanton and find that the tunneling rate reduces to the General Relativity (GR) value, even though the action value is different by a constant. We give a thorough analysis of the singular Vilenkin instanton and the Hawking-Turok instanton with a quadratic scalar field potential in the EiBI theory. In both cases, we find that the singularity can be avoided in the sense that the physical metric, its scalar curvature and the scalar field are regular under some parameter restrictions, but there is a curvature singularity of the auxiliary metric compatible with the connection. We find that the on-shell action is finite and the probability does not reduce to its GR value. We also find that the Vilenkin instanton in the EiBI theory would still cause the instability of the Minkowski space, similar to that in GR, and this is observationally inconsistent. This result suggests that the singularity of the auxiliary metric may be problematic at the quantum level and that these instantons should be excluded from the path integral.

The European Physical Journal C, 2019

There have been various interpretations of Hawking radiation proposed based on the perturbative approach, and all have confirmed Hawking's original finding. One major conceptual challenge of Hawking evaporation is the associated black hole information loss paradox, which remains unresolved. A key factor to the issue is the endstage of the black hole evaporation. Unfortunately by then the evaporation process becomes non-perturbative. Aspired to provide a tool for the eventual solution to this problem, here we introduce a new interpretation of Hawking radiation as the tunneling of instantons. We study instantons of a massless scalar field in Einstein gravity. We consider a complex-valued instanton that connects an initial pure black hole state to a black hole with a scalar field that represents the Hawking radiation at future null infinity, where its action depends only on the areal entropy difference. By comparing it with several independent approaches to Hawking radiation in the perturbative limit, we conclude that Hawking radiation may indeed be described by a family of instantons. Since the instanton approach can describe non-perturbative processes, we hope that our new interpretation and holistic method may shed lights on the information loss problem.

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.

Physical Review D, 2014

The Euclidean or Bunch-Davies O(4, 1) invariant 'vacuum' state of quantum fields in global de Sitter space is shown to be unstable to small perturbations, even for a massive free field with no self-interactions. There are perturbations of this state with arbitrarily small energy density at early times that is exponentially blueshifted in the contracting phase of 'eternal' de Sitter space, and becomes large enough to disturb the classical geometry through the semiclassical Einstein eqs. at later times. In the closely analogous case of a constant, uniform electric field, a time symmetric state equivalent to the de Sitter invariant one is constructed,

Physical Review D, 2000