Matrix Model Approach to Cosmology

Abstract

We perform a systematic search for rotationally invariant cosmological solutions to matrix models, or more specifically the bosonic sector of Lorentzian IKKT-type matrix models, in dimensions $d$ less than ten, specifically $d=3$ and $d=5$. After taking a continuum (or commutative) limit they yield $d-1$ dimensional space-time surfaces, with an attached Poisson structure, which can be associated with closed, open or static cosmologies. For $d=3$, we obtain recursion relations from which it is possible to generate rotationally invariant matrix solutions which yield open universes in the continuum limit. Specific examples of matrix solutions have also been found which are associated with closed and static two-dimensional space-times in the continuum limit. The solutions provide for a matrix resolution of cosmological singularities. The commutative limit reveals other desirable features, such as a solution describing a smooth transition from an initial inflation to a noninflationary era. Many of the $d=3$ solutions have analogues in higher dimensions. The case of $d=5$, in particular, has the potential for yielding realistic four-dimensional cosmologies in the continuum limit. We find four-dimensional de Sitter $d{S}^4$ or anti-de Sitter $Ad{S}^4$ solutions when a totally antisymmetric term is included in the matrix action. A nontrivial Poisson structure is attached to these manifolds which represents the lowest order effect of noncommutativity. For the case of $Ad{S}^4$, we find one particlular limit where the lowest order noncommutativity vanishes at the boundary, but not in the interior.

42 pages, 6 figures, reference added

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Cited by in corpus (23)

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• Signature change in matrix model solutions
• Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
• Non-commutative $Ad{S}_2/CF{T}_1$ duality: the case of massless scalar fields
• Fermions on curved backgrounds of matrix models
• The emergence of expanding space-time and intersecting D-branes from classical solutions in the Lorentzian type IIB matrix model
• One-loop effective action of the IKKT model for cosmological backgrounds
• On the structure of the emergent 3d expanding space in the Lorentzian type IIB matrix model
• Non-commutative $Ad{S}_2/CF{T}_1$ duality: the case of massive and interacting scalar fields
• Fuzzy $C{P}^2$ Space-Times
• Universality and the dynamical space-time dimensionality in the Lorentzian type IIB matrix model
• Dark Energy from the Fifth Dimension
• Cosmic acceleration in Regge-Teitelboim gravity
• A new method for probing the late-time dynamics in the Lorentzian type IIB matrix model
• Asymptotic commutativity of quantized spaces: the case of ${\mathbb{CP}}^{p,q}$
• Exact solutions for scalars and spinors on quantized (Euclidean) $Ad{S}_2$ and the correspondence principle
• Fuzzy de Sitter Space from kappa-Minkowski Space in Matrix Basis
• Spatially flat cosmological quantum spacetimes
• Exploring the gravity sector of emergent higher-spin gravity: effective action and a solution