Gravitational waves in the spectral action of noncommutative geometry

The noncommutative spectral action extends our familiar notion of commutative spaces, using the data encoded in a spectral triple on an almost commutative space. Varying a rather simple action, one can derive all of the standard model of particle physics in this setting, in addition to a modified version of Einstein-Hilbert gravity. In this letter we use observations of pulsar timings, assuming that no deviation from General Relativity has been observed, to constrain the gravitational sector of this theory. Whilst the bounds on the coupling constants remain rather weak, they are comparable to existing bounds on deviations from General Relativity in other settings and are likely to be further constrained by future observations.

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“…(2). The general first order solution for a perturbation against a Minkowski background is [10] h µν (r, t) = 4Gβ…”

Section: Introductionmentioning

confidence: 99%

Constraining the Noncommutative Spectral Action via Astrophysical Observations

2010

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“…Since running towards lower energies implies that nonperturbative effects in the spectral action cannot be any longer neglected, any results based on the asymptotic expansion and on renormalisation group analysis can only hold for early universe cosmology. Hence, the spectral action at the unification scale Λ offers a framework to investigate early universe cosmological models [7,8,9,10,11,12]. For later times, one should consider the full spectral action, a direction which requires the development of nontrivial mathematical tools.…”

Section: Elements Of Noncommutative Spectral Geometrymentioning

confidence: 99%

“…One can impose an upper limit to the moment f 0 , by studying the energy lost to gravitational radiation by orbiting binaries [11,12]. Considering linear perturbations around a Minkowski background metric, the equations of motion read [12] …”

Section: Cosmological Consequences Of the Noncommutative Spectral Geomentioning

confidence: 99%

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Cosmology within Noncommutative Spectral Geometry

Sakellariadou¹

2011

Proceedings of Corfu Summer Institute on Elementary Particles and Physics - Workshop on Non Commutative Field Theory and Gravit

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Close to the Planck energy scale, the quantum nature of space-time reveals itself and all forces, including gravity, should be unified so that all interactions correspond to just one underlying symmetry. In the absence of a full quantum gravity theory, one may follow an effective approach and consider space-time as the product of a four-dimensional continuum compact Riemanian manifold by a tiny discrete finite noncommutative space. Since all available data are of a spectral nature, one may argue that it is more appropriate to apply the spectral action principle in this almost commutative space. Following this procedure one obtains an elegant geometric explanation for the most successful particle physics model, namely the standard model (and supersymmetric extensions) of electroweak and strong interactions in all its details, as determined by experimental data. Moreover, since this gravitational theory lives by construction at very high energy scales, it offers a perfect framework to address some of the early universe cosmological questions still awaiting for an answer. After introducing some of the main mathematical elements of noncommutative spectral geometry, I will discuss various cosmological and phenomenological consequences of this theory, focusing in particular on constraints imposed on the gravitational sector of the theory.

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“…Cosmological implications of the spectral action, based on the asymptotic expansion, were considered in [18], [20], [23], [24], [25], [26]. For recent developments in the case of Robertson-Walker metrics see [9].…”

Section: 4mentioning

confidence: 99%

Coupling of gravity to matter, spectral action and cosmic topology

Ćaćić¹,

Marcolli²,

Teh³

2014

J. Noncommut. Geom.

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Abstract. We consider a model of modified gravity based on the spectral action functional, for a cosmic topology given by a spherical space form, and the associated slow-roll inflation scenario. We consider then the coupling of gravity to matter determined by an almost-commutative geometry over the spherical space form. We show that this produces a multiplicative shift of the amplitude of the power spectra for the density fluctuations and the gravitational waves, by a multiplicative factor equal to the total number of fermions in the matter sector of the model. We obtain the result by an explicit nonperturbative computation, based on the Poisson summation formula and the spectra of twisted Dirac operators on spherical space forms, as well as, for more general spacetime manifolds, using a heat-kernel computation. Contents

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Gravitational waves in the spectral action of noncommutative geometry

Cited by 44 publications

References 21 publications

Constraining the Noncommutative Spectral Action via Astrophysical Observations

Constraining the Noncommutative Spectral Action via Astrophysical Observations

Cosmology within Noncommutative Spectral Geometry

Coupling of gravity to matter, spectral action and cosmic topology

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