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Abstract In light of the recent swampland conjectures, we explore quantum cosmology and eternal inflation beyond the slow roll regime. We consider a model of a closed universe with a scalar field ϕ in the framework of tunneling approach to quantum cosmology. The scalar field potential is assumed to have a maximum at ϕ = 0 and can be approximated in its vicinity as V ( ϕ )≈ 3 H 2 - 1/2 m 2 ϕ 2 . Using the instanton method, we find that for m < 2 H the dominant nucleation channel for the universe is tunneling to a homogeneous, spherical de Sitter space. For larger values of m / H , the most probable tunneling is to an inhomogeneous closed universe with a domain wall wrapped around its equator. We determine the quantum state of the field ϕ in the nucleated universe by solving the Wheeler-DeWitt equation with tunneling boundary conditions. Our results agree with earlier work which assumed a slow-roll regime m ≪ H . We finally show that spherical universes nucleating with m < 2 H undergo stochastic eternal inflation with inflating regions forming a fractal of dimension d > 2. For larger values of m the field ϕ is unstable with respect to formation of domain walls and cannot be described by a perturbative stochastic approach. 

Abstract We use a path-integral approach to study the tunneling wave function in quantum cosmology with spatial topology S 1 × S 2 and positive cosmological constant (the Kantowski-Sachs model). If the initial scale factors of both S 1 and S 2 are set equal to zero, the wave function describes (semiclassically) a universe originating at a singularity. This may be interpreted as indicating that an S 1 × S 2 universe cannot nucleate out of nothing in a non-singular way. Here we explore an alternative suggestion by Halliwell and Louko that creation from nothing corresponds in this model to setting the initial volume to zero. We find that the only acceptable version of this proposal is to fix the radius of S 1 to zero, supplementing this with the condition of smooth closure (absence of a conical singularity). The resulting wave function predicts an inflating universe of high anisotropy, which however becomes locally isotropic at late times. Unlike the de Sitter model, the total nucleation probability is not exponentially suppressed, unless a Gauss-Bonnet term is added to the action. 

Abstract We study quantum cosmology of the 2 D Jackiw-Teitelboim (JT) gravity with Λ > 0 and calculate the Hartle-Hawking (HH) wave function for this model in the minisuperspace framework. Our approach is guided by the observation that the JT dynamics can be mapped exactly onto that of the Kantowski-Sachs (KS) model describing a homogeneous universe with spatial sections of S 1 × S 2 topology. This allows us to establish a JT-KS correspondence between the wave functions of the models. We obtain the semiclassical Hartle-Hawking wave function by evaluating the path integral with appropriate boundary conditions and employing the methods of Picard-Lefschetz theory. The JT-KS connection formulas allow us to translate this result to JT gravity, define the HH wave function and obtain a probability distribution for the dilaton field.