Noncommutative spectral geometry, algebra doubling, and the seeds of quantization

Abstract. Noncommutative spectral geometry offers a purely geometric explanation for the standard model of strong and electroweak interactions, including a geometric explanation for the origin of the Higgs field. Within this framework, the gravitational, the electroweak and the strong forces are all described as purely gravitational forces on a unified noncommutative space-time. In this study, we infer a constraint on one of the three free parameters of the model, namely the one characterising the coupling constants at unification, by linearising the field equations in the limit of weak gravitational fields generated by a rotating gravitational source, and by making use of recent experimental data. In particular, using data obtained by Gravity Probe B, we set a lower bound on the Weyl term appearing in the noncommutative spectral action, namely β 10 −6 m −1 . This constraint becomes stronger once we use results from torsion balance experiments, leading to β 10 4 m −1 . The latter is much stronger than any constraint imposed so far to curvature squared terms.

show abstract

“…of quantisation [4]. More recently, it has been also shown [5] that this structure can account for neutrino mixing [1,6].…”

mentioning

confidence: 86%

Constraints on noncommutative spectral action from Gravity Probe B and torsion balance experiments

Lambiase

Sakellariadou

Stabile

2013

J. Cosmol. Astropart. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The noncommutative nature of F is given secondly, the relation of NCSG to the gauge structure of the theory and to dissipation, summarising the results of Ref. [14]. …”

Section: Elements Of Noncommutative Spectral Geometrymentioning

confidence: 98%

Noncommutative spectral geometry: a short review

Sakellariadou

2013

J. Phys.: Conf. Ser.

Self Cite

View full text Add to dashboard Cite

We review the noncommutative spectral geometry, a gravitational model that combines noncommutative geometry with the spectral action principle, in an attempt to unify General Relativity and the Standard Model of electroweak and strong interactions. Despite the phenomenological successes of the model, the discrepancy between the predicted Higgs mass and the current experimental data indicate that one may have to go beyond the simple model considered at first. We review the current status of the phenomenological consequences and their implications. Since this model lives by construction at high energy scales, namely at the Grand Unified Theories scale, it provides a natural framework to investigate early universe cosmology. We briefly review some of its cosmological consequences.

show abstract

“…As we have shown in Refs. [18,19] this doubling is intimately related to dissipation, gauge field structure, neutrino mixing, while it incorporates the seeds of quantisation.…”

Section: Cosmological Consequences Through the Effective Friedmann Eqmentioning

confidence: 99%

Quantum Gravity and Cosmology: an intimate interplay

Sakellariadou

2017

J. Phys.: Conf. Ser.

Self Cite

View full text Add to dashboard Cite

Abstract. I will briefly discuss three cosmological models built upon three distinct quantum gravity proposals. I will first highlight the cosmological rôle of a vector field in the framework of a string/brane cosmological model. I will then present the resolution of the big bang singularity and the occurrence of an early era of accelerated expansion of a geometric origin, in the framework of group field theory condensate cosmology. I will then summarise results from an extended gravitational model based on non-commutative spectral geometry, a model that offers a purely geometric explanation for the standard model of particle physics. IntroductionMost of the fundamental questions in cosmology -which for a long time belonged to the realm of philosophy -can now be addressed within a physical theory and tested against increasingly accurate observational data. We live the golden age of cosmology. Still, fundamental puzzles remain. The most obvious is what, if anything, happened before the big bang? Another is what is the universe made of? Standard cosmology is formulated within the framework of Einstein's general theory of relativity. Notwithstanding, general relativity is not adequate to explain the earliest stages of cosmic existence, and cannot provide an explanation for the big bang itself. The reason is that quantum mechanics must have played a rôle at sufficiently early times. The majority of early universe cosmological models are studied at a semi-classical level, hence they leave basic questions such as the beginning of the universe, and the origin of inflation (or of alternative models) unanswered. Modern early universe cosmology is in the need of a rigorous underpinning in quantum gravity. More precisely, quantum gravity offers the appropriate framework to address fundamental questions such as the origin of the space-time continuum and its effective dynamics, and the pictures of the earliest moments of the universe which emerge. These pictures must include an approximately homogeneous background and superimposed perturbations. In return, cosmological data represent the best (if not the only) chance for testing quantum gravity, thus guiding the formulation of the complete fundamental theory.Quantum gravity proposals belong to two classes, they are either top-down or bottom-up. In the former class belong approaches like string/M-theory or a variant of non-perturbative approach to quantum gravity, like loop quantum gravity or group field theory. In the latter one belong the proposal of non-commutative (spectral) geometry, and that of asymptotic safety. String theory may provide the underlying theory required to resolve questions such as the initial

show abstract

Noncommutative spectral geometry, algebra doubling, and the seeds of quantization

Cited by 36 publications

References 48 publications

Constraints on noncommutative spectral action from Gravity Probe B and torsion balance experiments

Constraints on noncommutative spectral action from Gravity Probe B and torsion balance experiments

Noncommutative spectral geometry: a short review

Quantum Gravity and Cosmology: an intimate interplay

Contact Info

Product

Resources

About