Noncommutative spectral geometry: a short review

Sakellariadou, Mairi

doi:10.1088/1742-6596/442/1/012015

Cited by 6 publications

(5 citation statements)

References 30 publications

(44 reference statements)

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“…Following however a consistent treatment of both the fermionic and the bosonic parts of the action [420] one obtains nontrivial corrections leading to nonminimal fermion couplings and a potentially rich phenomenology. Non-commutative spectral geometry leads to an extended gravitational theory, where the gravitational sector includes additional terms beyond the ones of the Einstein-Hilbert action [421]. Their cosmological consequences and constraints from observational data have been discussed in [422][423][424][425].…”

Section: Relative Locality and Born Geometrymentioning

confidence: 99%

Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review

Addazi,

Alvarez-Muniz,

Batista

et al. 2021

Preprint

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The exploration of the universe has recently entered a new era thanks to the multi-messenger paradigm, characterized by a continuous increase in the quantity and quality of experimental data that is obtained by the detection of the various cosmic messengers (photons, neutrinos, cosmic rays and gravitational waves) from numerous origins. They give us information about their sources in the universe and the properties of the intergalactic medium. Moreover, multi-messenger astronomy opens up the possibility to search for phenomenological signatures of quantum gravity. On the one hand, the most energetic events allow us to test our physical theories at energy regimes which are not directly accessible in accelerators; on the other hand, tiny effects in the propagation of very high energy particles could be amplified by cosmological distances. After decades of merely theoretical investigations, the possibility of obtaining phenomenological indications of Planck-scale effects is a revolutionary step in the quest for a quantum theory of gravity, but it requires cooperation between different communities of physicists (both theoretical and experimental). This review, prepared within the COST Action CA18108 "Quantum gravity phenomenology in the multi-messenger approach", is aimed at promoting this cooperation by giving a state-of-the art account of the interdisciplinary expertise that is needed in the effective search of quantum gravity footprints in the production, propagation and detection of cosmic messengers.

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Section: Relative Locality and Born Geometrymentioning

confidence: 99%

Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review

Addazi,

Alvarez-Muniz,

Batista

et al. 2021

Preprint

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“…In almost-commutative geometry [102] (see [106][107][108][109] for reviews) the possible spaces are restricted such that they contain Riemannian spin manifolds M . These are spaces that locally look like the Euclidean space R d and a Riemannian metric g µν exists as well as spinors are admitted.…”

Section: Almost-commutative Geometry and Spectral Actionsmentioning

confidence: 99%

Asymptotically safe f(R)-gravity coupled to matter I: The polynomial case

2018

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We use the functional renormalization group equation for the effective average action to study the non-Gaussian renormalization group fixed points (NGFPs) arising within the framework of f (R)-gravity minimally coupled to an arbitrary number of scalar, Dirac, and vector fields. Based on this setting we provide comprehensible estimates which gravity-matter systems give rise to NGFPs suitable for rendering the theory asymptotically safe. The analysis employs an exponential split of the metric fluctuations and retains a 7-parameter family of coarse-graining operators allowing the inclusion of non-trivial endomorphisms in the regularization procedure.For vanishing endomorphisms, it is established that gravity coupled to the matter content of the standard model of particle physics and many beyond the standard model extensions exhibit NGFPs whose properties are strikingly similar to the case of pure gravity: there are two UV-relevant directions and the position and critical exponents converge rapidly when higher powers of the scalar curvature are included.Conversely, none of the phenomenologically interesting gravity-matter systems exhibits a stable NGFP when a Type II coarse graining operator is employed. Our analysis resolves this tension by demonstrating that the NGFPs seen in the two settings belong to different universality classes.

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“…In NCSG, a noncommutative geometric space is encoded by a spectral triple (A, H, D) where the algebra A is the algebra of functions that interact with the inverse line element D, by acting in the same Hilbert space H, where D is an unbounded self-adjoint operator [40]. It is explicitly stated in [41] that the NCSG approach is compatible with the noncommutative approach based upon [ ] . The reason being that in the literature a noncommutative space is often of Moyal type, involving noncommutative tori or Moyal planes and the Euclidean version of Moyal noncommutative field theory is compatible with the spectral triples formulation of noncommutative geometry.…”

Section: Comparison To Other Work Based On Noncommutative Spectral Gmentioning

confidence: 99%

Gravitational radiation in dynamical noncommutative spaces

Alavi¹,

Nasab²

2016

Gen Relativ Gravit

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We investigate gravitational radiation in dynamical noncommutative spaces. By including corrections to the gravitational potential due to dynamical noncommutativity, we calculate the power in gravitational radiation and use observational data to place an upper bound on the noncommutativity parameter. We also study quantum interference induced by gravitational potential in the usual and dynamical noncommutative spaces, and compare the resulting phase difference in these cases with that in commutative space.

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Noncommutative spectral geometry: a short review

Cited by 6 publications

References 30 publications

Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review

Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review

Asymptotically safe f(R)-gravity coupled to matter I: The polynomial case

Gravitational radiation in dynamical noncommutative spaces

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