Integrable Multicomponent Perfect Fluid Multidimensional Cosmology II: Scalar Fields

Abstract

We consider anisotropic cosmological models with an universe of dimension 4 or more, factorized into n ≥ 2 Ricci-flat spaces, containing an m-component perfect fluid of m noninteracting homogeneous minimally coupled scalar fields under special conditions. We describe the dynamics of the universe: It has a Kasner-like behaviour near the singularity and isotropizes during the expansion to infinity.Some of the considered models are integrable, and classical as well as quantum solutions are found. Some solutions produce inflation from "nothing". There exist classical asymptotically anti-de Sitter wormholes, and quantum wormholes with discrete spectrum.

Integrable scalar cosmologies with matter and curvature

“…7 for the plot of the map ϕ ∈ R → V(ϕ)/V ). 20 Let us give some hints about the derivation of the asymptotic expansion (4.2.77), understanding that the maximal domain of definition of the solution is I = (0, +∞) as in Eq. (4.2.71).…”

“…The same authors extended these results to the case of a field with non-minimal coupling to gravity in [9]. In 1996 Zhuk et al [20,40] (see also [21]) examined cosmological models where the spacetime was the product of a time line with an arbitrary number of Einstein spaces of arbitrary dimensions, and the content of the universe was described by a family of scalar fields. The scalar fields were assumed to be minimally-coupled to gravity, self-interacting with a potential to be specified (yet, with no mutual interactions), and to fulfill each one a prescribed equation of state.…”

“…With the notable exceptions of [4,20,40] (and [21]), all papers [1,7,8,9,30,32,34] mentioned above deal with spacetimes of dimension 3 + 1.…”

Squeezed Wave Packets in Quantum Cosmology

“…The issue of multi-dimensional cosmology has attracted much attention and many papers has been appeared in the literature by numerous authors [1][2][3]. These efforts have begun by Kaluza and Klein who were interested to geometrically unify the gravitation and electromagnetism via introducing one undetectable extra dimension.…”

Quantum noncommutative multidimensional cosmology

“…Since then, a large body of research work has been devoted to the study of multidimensional models inspired by Kaluza and Klein. The idea of extra dimensions have also been employed to suggest possible resolutions to some of the important problems that cosmology has been facing [22][23][24], namely, the mass hierarchy and cosmological constant problem. As was mentioned above, over the recent past, the notion of noncommutativity has been playing an increasingly important role in cosmology and, naturally, the Kaluza-Klein theory would have a prominent part to play in this regard.…”