Noncommutative de Sitter and FRW spaces

Burić, Maja; Madore, J.

doi:10.1140/epjc/s10052-015-3729-6

Cited by 40 publications

(53 citation statements)

References 27 publications

(38 reference statements)

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“…It is natural to wonder about de Sitter branes. There are indeed candidates for fuzzy de Sitter space based on the principal series representations of SO(4, 1) [12,32,[39][40][41][42], some of which should be solutions of the matrix model for m 2 0 = m 2 ; see also [43] for related work. However then the effective metric would coincide with the induced one, without BB.…”

Section: Discussionmentioning

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: Discussionmentioning

confidence: 99%

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

Steinacker

2018

J. High Energ. Phys.

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“…The general idea is to work on an extended R 3 λ fourdimensional space and apply the gauge theory procedure on it. The last direction is to incorporate the gauge group and the four-dimensional non-commutative space into a larger symmetry group, in the spirit of [41,42].…”

Section: Discussionmentioning

confidence: 99%

Gravity as a Gauge Theory on Three-Dimensional Noncommutative spaces

Jurman¹,

Manolakos²,

Manousselis³

et al. 2018

Proceedings of Corfu Summer Institute 2017 "Schools and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2017)

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We plan to translate the successful description of three-dimensional gravity as a gauge theory in the noncommutative framework, making use of the covariant coordinates. We consider two specific three-dimensional fuzzy spaces based on SU(2) and SU(1,1), which carry appropriate symmetry groups. These are the groups we are going to gauge in order to result with the transformations of the gauge fields (dreibein, spin connection and two extra Maxwell fields due to noncommutativity), their corresponding curvatures and eventually determine the action and the equations of motion. Finally, we verify their connection to three-dimensional gravity.

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“…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%

Discrete fuzzy de Sitter cosmology

Burić

Latas

2019

Phys. Rev. D

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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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Noncommutative de Sitter and FRW spaces

Cited by 40 publications

References 27 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

Gravity as a Gauge Theory on Three-Dimensional Noncommutative spaces

Discrete fuzzy de Sitter cosmology

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