[Paper Review] Euclidean wormholes in Gauss-Bonnet-dilaton gravity

Xiao Yan Chew, Gansukh Tumurtushaa+1 more|arXiv (Cornell University)|Jun 8, 2020

Cosmology and Gravitation Theories4 citations

TL;DR

This paper investigates Euclidean wormhole solutions in Gauss-Bonnet-dilaton gravity as a quantum gravitational mechanism for the universe's origin from nothing. Using Wick-rotated Euclidean path integrals, it shows that these wormholes—especially with dilaton fields over potential barriers—have higher tunneling probabilities than Hawking-Moss instantons, even without slow-roll conditions, making them a more probable scenario for cosmogony in this modified gravity framework.

ABSTRACT

We investigate Euclidean wormholes in Gauss-Bonnet-dilaton gravity to explain the creation of the universe from nothing. We considered two types of dilaton couplings (i.e., the string-inspired model and the Gaussian model) and we obtained qualitatively similar results. There can exist Euclidean wormholes that explain the possible origin of our universe, where the dilaton field is located over the barrier of dilaton potential. This solution can exist even if dilaton potential does not satisfy slow-roll conditions. In addition, the probability is higher than that of the Hawking-Moss instanton with the same final condition. Therefore, Euclidean wormholes in Gauss-Bonnet-dilaton gravity are a possible and probable scenario, which explains the origin of our universe.

Motivation & Objective

• To explore whether Euclidean wormholes in Gauss-Bonnet-dilaton gravity can serve as viable instanton solutions for the universe's quantum creation.
• To assess the tunneling probability of these wormhole solutions relative to standard Hawking-Moss instantons under the same final conditions.
• To investigate the role of dilaton field dynamics, particularly when located over a potential barrier, and its implications for cosmogony.
• To determine whether such solutions remain viable in the sub-Planckian regime and avoid theoretical instabilities.
• To evaluate the physical plausibility and observational relevance of these solutions in the context of quantum gravity and early-universe cosmology.

Proposed method

• Employing the Euclidean path-integral approach with Wick rotation to the action, computing the wave function of the universe via steepest-descent approximation.
• Using the homogeneous analytic continuation method to map Euclidean solutions to Lorentzian spacetimes, enabling physical interpretation.
• Solving the equations of motion for a 4D Gauss-Bonnet-dilaton gravity model with two distinct dilaton couplings: string-inspired and Gaussian forms.
• Evaluating the Euclidean action integral $ B = rac{1}{2} ext{Re} ig( au_{ ext{max}} ig) imes ext{Lagrangian} $ to compute tunneling probabilities $ P ightarrow e^{-2B} $.
• Analyzing the behavior of $ B $ across parameter space, particularly varying $ ho $, $ u $, $ ho_0 $, $ u_0 $, $ ho_1 $, $ u_1 $, $ ho_2 $, $ u_2 $, and $ c $, to assess stability and probability.
• Comparing the resulting instanton probabilities with those of the Hawking-Moss model to determine relative likelihoods.

Experimental results

Research questions

• RQ1 Can Euclidean wormhole solutions exist in Gauss-Bonnet-dilaton gravity that describe the universe's quantum creation from nothing?
• RQ2 Do these wormhole solutions have higher tunneling probabilities than Hawking-Moss instantons under identical final conditions?
• RQ3 Is the existence of such wormholes dependent on the slow-roll approximation for the dilaton field?
• RQ4 What is the role of the dilaton field being located over a potential barrier rather than in a minimum?
• RQ5 Can these solutions be realized in the sub-Planckian regime without introducing theoretical instability?

Key findings

• Euclidean wormhole solutions exist in Gauss-Bonnet-dilaton gravity even when the dilaton field is located over a potential barrier, not in a minimum, and without satisfying slow-roll conditions.
• The tunneling probability for these wormhole solutions is higher than that of Hawking-Moss instantons with the same final state, as evidenced by a more negative Euclidean action $ B $.
• For the case $ c o 0 $, a long-stretched instanton emerges instead of a wormhole, which remains physically viable under homogeneous analytic continuation and does not lead to naked singularities.
• The probability increases with larger $ ho $ (related to coupling strength) and decreases with larger $ c $, indicating a preference for small $ c $ and moderate coupling parameters.
• Solutions exist in both sub-Planckian and super-Planckian regimes, but super-Planckian values may lead to theoretical instability, requiring further study in full quantum gravity.
• Perturbations from these wormhole instantons may not yield a scale-invariant Bunch-Davies state, offering a potential observational signature distinguishable from standard inflationary models.