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Chaney, A.; Stern, A.

doi:10.1103/physrevd.95.046001

Cited by 9 publications

(18 citation statements)

References 41 publications

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“…[12][13][14][15][16][17]. Even compact solutions were found in [18,19], where it was pointed out that the induced metric on the brane can change from Euclidean to Minkowski signature. However, this alone is not sufficient to obtain a Big Bang, and it does not imply a rapid expansion.…”

Section: Jhep02(2018)033mentioning

confidence: 99%

Cosmological space-times with resolved Big Bang in Yang-Mills matrix models

Steinacker

2018

J. High Energ. Phys.

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We present simple solutions of IKKT-type matrix models that can be viewed as quantized homogeneous and isotropic cosmological space-times, with finite density of microstates and a regular Big Bang (BB). The BB arises from a signature change of the effective metric on a fuzzy brane embedded in Lorentzian target space, in the presence of a quantized 4-volume form. The Hubble parameter is singular at the BB, and becomes small at late times. There is no singularity from the target space point of view, and the brane is Euclidean "before" the BB. Both recollapsing and expanding universe solutions are obtained, depending on the mass parameters.

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Section: Jhep02(2018)033mentioning

confidence: 99%

Cosmological space-times with resolved Big Bang in Yang-Mills matrix models

Steinacker

2018

J. High Energ. Phys.

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“…Due to the expansion of space, it is expected that the dominant configurations can be well approximated at late times by some classical solution of the Lorentzian type IIB matrix model. Indeed several types of classical solutions representing expanding space-time have been constructed [14][15][16][17][18][19][20][21]. Also, matrix configurations with various structures in the extra dimensions are considered to realize chiral fermions in the (3+1)d space-time.…”

Section: Introductionmentioning

confidence: 99%

On the structure of the emergent 3D expanding space in the Lorentzian type IIB matrix model

Aoki

Hirasawa

Ito

et al. 2019

Progress of Theoretical and Experimental Physics

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The emergence of (3+1)-dimensional expanding space-time in the Lorentzian type IIB matrix model is an intriguing phenomenon which was observed in Monte Carlo studies of this model. In particular, this may be taken as a support to the conjecture that the model is a nonperturbative formulation of superstring theory in (9+1) dimensions. In this paper we investigate the space-time structure of the matrices generated by simulating this model and its simplified versions, and find that the expanding part of the space is described essentially by the Pauli matrices. We argue that this is due to an approximation used in the simulation to avoid the sign problem, which actually amounts to replacing e iS b by e βS b (β > 0) in the partition function, where S b is the bosonic part of the action. We also discuss the possibility of obtaining a regular space-time with the (3+1)-dimensional expanding behavior in the original model with the correct e iS b factor.

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“…which is consistent with the requirement that |ζ 1 | 2 + |ζ 2 | 2 − 1 > 0. The induced metic in these coordinates has the Taub-NUT form (which was also true for the CP 2 solution [12])…”

Section: Eight-dimensional Matrix Modelmentioning

confidence: 71%

“…Tr denotes a trace, indices µ, ν, λ, ... are raised and lowered with the Lorentz metric η µν =diag(−, +, +), and the § As stated above, we assume to the background metric to be the su(2, 1) Cartan-Killing metric. Non-commutative CP 2 , and its deformations, were shown to solve an eight-dimensional Lorentzian matrix model with a different background metric in [12].…”

Section: Introductionmentioning

confidence: 99%

Signature change in matrix model solutions

Stern

2018

Phys. Rev. D

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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. * astern@ua.edu † cxu24@crimson.ua.edu arXiv:1808.07963v2 [hep-th] 18 Oct 2018 ‡ We thank J. Hoppe for bringing this to our attention.sphere, the Lorentzian region crudely describes a two-dimensional closed cosmology, complete with an initial and final singularity. In the case of the deformation of non-commutative (Euclidean) (A)dS 2 , the Lorentzian region describes a two-dimensional open cosmology.Natural extensions of these solutions to higher dimensions are the non-commutative complex projective spaces.[30]-[36] Since we wish to recover noncompact manifolds, as well as compact manifolds in the commutative limit, we should consider the indefinite versions of these non-commutative spaces, [37] as well as those constructed from compact groups. For four dimensional solutions, there are then three such candidates: non-commutative CP 2 , CP 1,1 and CP 0,2 . The latter two solve an eight-dimensional (massless) matrix model with indefinite background metric, specifically, the su(2, 1) Cartan-Killing metric. These solutions give a fixed signature after taking the commutative limit. So as with the previous examples, the massless matrix model yields no signature change. Once again, new solutions appear when a mass term is included, and they exhibit signature change, possibly multiple signature changes. These solutions include deformations of non-commutative CP 2 , CP 1,1 and CP 0,2 . § A deformed noncommutative CP 0,2 solution can undergo two signature changes, while a deformed non-commutative CP 2 solution can have up to three signature changes. Upon taking the commutative limit, the deformed non-commutative CP 1,1 and CP 0,2 solutions have regions with Lorentzian signature that describe expanding open space-time cosmologies, complete with a big bang singularity occurring at the signature change. The commutative limit of the deformed non-commutative CP 2 solution has a region with Lorentzian signature that describes a closed space-time cosmology, complete with initial/final singularities. Like the non-commutative H 4 solution found in [13], these solutions display extremely rapid expansion near the cosmolog...

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FuzzyCP2spacetimes

Cited by 9 publications

References 41 publications

Cosmological space-times with resolved Big Bang in Yang-Mills matrix models

Cosmological space-times with resolved Big Bang in Yang-Mills matrix models

On the structure of the emergent 3D expanding space in the Lorentzian type IIB matrix model

Signature change in matrix model solutions

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