Abstract
Various classical solutions to lower dimensional IKKT-like Lorentzian matrix models are examined in their commutative limit. Poisson manifolds emerge in this limit, and their associated induced and effective metrics are computed. Signature change is found to be a common feature of these manifolds when quadratic and cubic terms are included in the bosonic action. In fact, a single manifold may exhibit multiple signature changes. Regions with Lorentzian signature may serve as toy models for cosmological space-times, complete with cosmological singularities, occurring at the signature change. The singularities are resolved away from the commutative limit. Toy models of open and closed cosmological space-times are given in two and four dimensions. The four dimensional cosmologies are constructed from non-commutative complex projective spaces, and they are found to display a rapid expansion near the initial singularity.
Highlights
Signature change is believed to be a feature of quantum gravity [1,2,3,4,5,6,7,8,9,10]
We argue that signature change is a common feature of solutions to IKKT-type matrix models with indefinite background metrics, in particular, when mass terms are included in the matrix model action. (Mass terms have been shown to result from an IR regularization [16].) a single solution can exhibit multiple signature changes
We have obtained a number of new solutions to IKKT-type matrix models, which exhibit signature change in the commutative limit
Summary
Signature change is believed to be a feature of quantum gravity [1,2,3,4,5,6,7,8,9,10]. Signature change has been shown to result from certain solutions to matrix equations [11,12,13] These are the classical equations of motion that follow from Ishibashi, Kawai, Kitazawa, and Tsuchiya (IKKT)-type models [14] with a Lorentzian background target metric. The signature change occurs in the induced metrics of the continuous manifolds that emerge upon taking the commutative (or equivalently, continuum or semiclassical) limit of the matrix model solutions. It has been shown that toy cosmological models can be constructed for regions of the manifolds where the metric has a Lorentzian signature These regions can represent both open and closed cosmologies, complete with cosmological singularities that occur at the signature changes. We argue that signature change is a common feature of solutions to IKKT-type matrix models with indefinite background metrics, in particular, when mass terms are included in the matrix model action. It is known that there are zero mean curvature surfaces in threedimensional Minkowski space that change from being
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