Fuzzy de Sitter space

Burić, Maja; Latas, Duško; Nenadović, Luka

doi:10.1140/epjc/s10052-018-6432-6

Cited by 27 publications

(28 citation statements)

References 37 publications

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“…One of the problems which arises on simple non-commutative geometries is that they typically carry some Lorentz-breaking structure, which is well hidden classically, but tends to show up in the loop contributions. That problem can be avoided on covariant quantum spaces, such as fuzzy S 4 N , H 4 n , and similar spaces [27][28][29][30][31][32][33][34][35]. This class of spaces exhibits a rich extra structure, which typically leads to a higher-spin gauge theory [36][37][38].…”

Section: Introductionmentioning

confidence: 99%

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

Sperling¹,

Steinacker²

2019

J. High Energ. Phys.

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: 99%

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

Sperling¹,

Steinacker²

2019

J. High Energ. Phys.

101

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“…One way to see if noncommutativity improves the singularity structure of spacetime is to determine the spectra of coordinates, in this case τ and x i , or (x i ) 2 . As found in [6], spectra of x i are continuous in (ρ, s) representations; embedding time W 0 /l has discrete spectrum. Here we wish to find eigenvalues of the cosmic time.…”

Section: Fuzzy De Sitter Spacementioning

confidence: 61%

“…Our task is to study observable of time in cosmological model introduced in [5,6]. In commutative geometry, four-dimensional de Sitter space can be defined as an embedding in five-dimensional flat space [7],…”

Section: Fuzzy De Sitter Spacementioning

confidence: 99%

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Discrete fuzzy de Sitter cosmology

Burić

Latas

2019

Phys. Rev. D

Self Cite

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We analyze the spectrum of time observable in noncommutative cosmological model introduced in [5], defined by (ρ, s = 1 2 ) representation of the de Sitter group. We find that time has peculiar property:it is not self-adjoint, but appropriate restrictions to the space of physical states give self-adjoint extensions. Extensions have discrete spectrum with logarithmic distribution of eigenvalues, t n ∼ log n+const, where characterizes noncommutativity and the usual assumption is = P lanck . When calculated on physical states, radius of the universe is bounded below by 3 4 1 4 + ρ 2 , which resolves the big bang singularity. An immediate consequence of the model is a specific breaking of the original symmetry at the Planck scale. * majab@ipb.ac.rs, latas@ipb.ac.rs 1 arXiv:1903.08378v2 [hep-th]

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“…Comparing the presented approach with the similar approaches to the construction of non-commutative spheres and their pseudo-Riemaniann counterparts, [33][34][35][36][37][38][39][40][41][42] one should note that the presented approach determines a map only onto the half of de Sitter space.…”

Section: Resultsmentioning

confidence: 99%

Fuzzy de Sitter Space from kappa‐Minkowski Space in Matrix Basis

Jurman

2019

Fortschritte der Physik

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We consider the Lie group RκD generated by the Lie algebra of κ‐Minkowski space. Imposing the invariance of the metric under the pull‐back of diffeomorphisms induced by right translations in the group, we show that a unique right invariant metric is associated with RκD. This metric coincides with the metric of de Sitter space‐time. We analyze the structure of unitary representations of the group RκD relevant for the realization of the non‐commutative κ‐Minkowski space by embedding into (2D−1)‐dimensional Heisenberg algebra. Using a suitable set of generalized coherent states, we select the particular Hilbert space and realize the non‐commutative κ‐Minkowski space as an algebra of the Hilbert‐Schmidt operators. We define dequantization map and fuzzy variant of the Laplace‐Beltrami operator such that dequantization map relates fuzzy eigenvectors with the eigenfunctions of the Laplace‐Beltrami operator on the half of de Sitter space‐time.

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Fuzzy de Sitter space

Cited by 27 publications

References 37 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

Discrete fuzzy de Sitter cosmology

Fuzzy de Sitter Space from kappa‐Minkowski Space in Matrix Basis

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