October 31, 1995
We extend to multidimensional cosmology Vilenkin's prescription of tunnelling from nothing for the quantum origin of the observable Universe. Our model consists of a $D+4$-dimensional spacetime of topology ${\cal R}\times {\cal S}^3 \times{\cal S}^D$, with a scalar field (``chaotic inflaton'') for the matter component. Einstein gravity and Casimir compactification are assumed. The resulting minisuperspace is 3--dimensional. Patchwise we find an approximate analytic solution of the Wheeler--DeWitt equation through which we discuss the tunnelling picture and the probability of nucleation of the classical Universe with compactifying extra dimensions. Our conclusion is that the most likely initial conditions, although they do not lead to the compactification of the internal space, still yield (power-law) inflation for the outer space. The scenario is physically acceptable because the inner space growth is limited to $\sim 10^{11}$ in 100 e-foldings of inflation, starting from the Planck scale.
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December 2, 1996
We give a detailed presentation of a recently proposed mechanism of generating the energy scale of inflation by loop effects in quantum cosmology. We discuss the quantum origin of the early inflationary Universe from the no-boundary and tunneling quantum states and present a universal effective action algorithm for the distribution function of chaotic inflationary cosmologies in both of these states. The energy scale of inflation is calculated by finding a sharp probability p...
October 17, 1995
Quantum origin of the early inflationary Universe from the no-boundary and tunnelling quantum states is considered in the one-loop approximation of quantum cosmology. A universal effective action algorithm for the distribution function of chaotic inflationary cosmologies is derived for both of these states.The energy scale of inflation is calculated by finding a sharp probability peak in this distribution function for a tunnelling model driven by the inflaton field with large...
June 5, 1998
The Wheeler-DeWitt equation in the minisuperspace approximation is studied in four different models. Under certain circumstances each model leads to a tunneling potential and under the same circumstances the classical version of each model leads to inflation.
May 6, 1994
Multidimensional cosmological models with $n~(n > 1)$ Einstein spaces are discussed classically and with respect to canonical quantization. These models are integrable in the case of Ricci flat internal spaces. For negative curvature of the external space we find exact classical solutions modelling dynamical as well as spontaneous compactification of the internal spaces. Spontaneous compactification turns out to be an attractor solution. Solutions of the quantum Wheeler-DeWit...
January 12, 2001
A brief review of the modern state of quantum cosmology is presented as a theory of quantum initial conditions for inflationary scenario. The no-boundary and tunneling states of the Universe are discussed as a possible source of probability peaks in the distribution of initial data for inflation. It is emphasized that in the tree-level approximation the existence of such peaks is in irreconcilable contradiction with the slow roll regime -- the difficulty that is likely to be ...
April 18, 2002
This contribution consists of two parts. In the first part, I review the tunneling approach to quantum cosmology and comment on the alternative approaches. In the second part, I discuss the relation between quantum cosmology and eternal inflation. In particular, I discuss whether or not we need quantum cosmology in the light of eternal inflation, and whether or not quantum cosmology makes any testable predictions.
July 31, 2017
We present Euclidean wormhole solutions describing possible bridges within the multiverse. The study is carried out in the framework of the third quantization. The matter content is modelled through a scalar field which supports the existence of a whole collection of universes. The instanton solutions describe Euclidean solutions that connect baby universes with asymptotically de Sitter universes. We compute the tunnelling probability of these processes. Considering the curre...
April 28, 1998
In this paper we investigate a model of an inflationary universe in Kaluza-Klein theory, which is a four-dimensional de Sitter space plus a one-dimensional compactified internal space. We find that the energy scale for inflation can be predicted from the fine-structure constant in a self-consistent solution of the semi-classical Einstein equations including the Casimir effect. From the observed value of the fine-structure constant, we obtain an energy scale for inflation of $...
April 7, 1997
At the minisuperspace level of homogeneous models, the bare probability for a classical universe has a huge peak at small universes for the Hartle-Hawking `no-boundary' wavefunction, in contrast to the suppression at small universes for the `tunneling' wavefunction. If the probability distribution is cut off at the Planck density (say), this suggests that the former quantum state is inconsistent with our observations. For inhomogeneous models in which stochastic inflation can...
April 25, 2002
We show why the universe started in an unstable de Sitter state. The quantum origin of our universe implies one must take a `top down' approach to the problem of initial conditions in cosmology, in which the histories that contribute to the path integral, depend on the observable being measured. Using the no boundary proposal to specify the class of histories, we study the quantum cosmological origin of an inflationary universe in theories like trace anomaly driven inflation ...