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

Steinacker, Harold

doi:10.1007/jhep02(2018)033

Cited by 32 publications

(54 citation statements)

References 62 publications

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“…Nevertheless, some breaking of Lorentz invariance is bound to show up somewhere. The present M 3,1 n solution is somewhat different from (and in a sense dual to) the solution recently found in [39,44]. The present realization is preferred, because it allows to systematically organize and study the (linearized) fluctuation spectrum.…”

Section: Introductionmentioning

confidence: 65%

“…This is based on the fuzzy 4hyperboloid H 4 n , which is a quantization of the S 2 -bundle CP 1,2 → H 4 with the canonical Poisson structure on CP 1,2 . Fuzzy H 4 n was introduced in [48] and further developed in [44], and we briefly recapitulate the main results. As for any coadjoint orbit, the canonical quantization of CP 1,2 proceeds in terms of the operator algebra End(H n ) where H n is a suitable unitary irreducible representation (irrep) of SU (2, 2) ∼ = SO(4, 2).…”

Section: 2mentioning

confidence: 99%

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Covariant cosmological quantum space-time, higher-spin and gravity in the IKKT matrix model

Sperling¹,

Steinacker²

2019

J. High Energ. Phys.

Self Cite

101

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We discuss a (3+1)-dimensional covariant quantum space-time describing a FLRW cosmology with Big Bounce, obtained by a projection of the fuzzy hyperboloid H 4 n . This provides a background solution of the IKKT matrix model with mass term. We characterize the bosonic fluctuation spectrum, which consists of a tower of higherspin modes, truncated at n. The modes are organized in terms of an underlying SO(4, 2) structure group, which is broken to the SO(3, 1) isometry of the background. The resulting higher-spin gauge theory includes all degrees of freedom required for gravity, and should be well suited for quantization. All modes propagate with the same speed of light, even though local boost invariance is not manifest. The propagating metric perturbation modes comprise those of a massless graviton, as well as a scalar mode. Gauge invariance allows to obtain the analog of the linearized Einstein-Hilbert action, which is expected to be induced upon quantization.12 Note that SO(4, 2) should not be interpreted as conformal group on H 4 , rather it provides the organization of the higher-spin modes on H 4 and M 3,1 . 13 We will ignore the dependence on two sheets M ± for simplicity.

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Section: Introductionmentioning

confidence: 65%

Section: 2mentioning

confidence: 99%

Covariant cosmological quantum space-time, higher-spin and gravity in the IKKT matrix model

Sperling¹,

Steinacker²

2019

J. High Energ. Phys.

Self Cite

101

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“…The Universe at t > 0 can be obtained by analytic continuation from the negative t region, where the metric has Euclidean signature. In this scenario, the Big Bang (at t = 0) represents the point of the phase transition from the Euclidean to Minkowski signature, which is similar to that, say, in [11][12][13][14] (an example of such transition in condensed matter can be found e.g. in Ref.…”

Section: Euclidean Signature Universe and Spontaneously Broken Cmentioning

confidence: 94%

Comment to the CPT-Symmetric Universe: Two Possible Extensions

Volovik

2019

Jetp Lett.

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In Ref. 1 the antispacetime Universe was suggested as the analytic continuation of our Universe across the Big Bang singularity in conformal time. We consider two different scenarios of analytic continuation. In one of them the analytic continuation is extended to the temperature of the system. This extension suggests that if such analytic continuation is valid, then it is possible that the initial stage of the evolution of the Universe on our side of the Big Bang was characterized by the negative temperature. In the second scenario, the analytic continuation is considered in the proper time. In this scenario the Big Bang represents the bifurcation point at which the Z2 symmetry between the spacetime and antispacetime is spontaneously broken.

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

Cited by 32 publications

References 62 publications

Covariant cosmological quantum space-time, higher-spin and gravity in the IKKT matrix model

Covariant cosmological quantum space-time, higher-spin and gravity in the IKKT matrix model

Comment to the CPT-Symmetric Universe: Two Possible Extensions

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

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