Early universe models from noncommutative geometry

Marcolli, Matilde; Pierpaoli, E.

doi:10.4310/atmp.2010.v14.n5.a2

Cited by 46 publications

(87 citation statements)

References 47 publications

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“…It is defined in terms of the spectrum of the Dirac operator, and it recovers the usual Einstein-Hilbert action with cosmological term, along with modified gravity terms (Weyl curvature conformal gravity, Gauss-Bonnet gravity), in an asymptotic expansion in the energy scale. As a model of gravity, the spectral action was used in recent years as a possible source of new early universe models and inflationary mechanisms, [4,22,36,[42][43][44][45][46][47][48].…”

Section: Jhep10(2015)085mentioning

confidence: 99%

Spectral action for Bianchi type-IX cosmological models

Fan

Fathizadeh

Marcolli

2015

J. High Energ. Phys.

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A rationality result previously proved for Robertson-Walker metrics is extended to a homogeneous anisotropic cosmological model, namely the Bianchi type-IX minisuperspace. It is shown that the Seeley-de Witt coefficients appearing in the expansion of the spectral action for the Bianchi type-IX geometry are expressed in terms of polynomials with rational coefficients in the cosmic evolution factors w 1 (t), w 2 (t), w 3 (t), and their higher derivates with respect to time. We begin with the computation of the Dirac operator of this geometry and calculate the coefficients a 0 , a 2 , a 4 of the spectral action by using heat kernel methods and parametric pseudodifferential calculus. An efficient method is devised for computing the Seeley-de Witt coefficients of a geometry by making use of Wodzicki's noncommutative residue, and it is confirmed that the method checks out for the cosmological model studied in this article. The advantages of the new method are discussed, which combined with symmetries of the Bianchi type-IX metric, yield an elegant proof of the rationality result.

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Section: Jhep10(2015)085mentioning

confidence: 99%

Spectral action for Bianchi type-IX cosmological models

Fan

Fathizadeh

Marcolli

2015

J. High Energ. Phys.

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“…(2) There is a simple and efficient analogue in noncommutative geometry for the modification of the conformal structure encoded by a Beltrami differential ( [18]). Finally there are interesting developments on cosmology [47], [53] which open a new line of investigations where the KMS condition should play a leading role in the analysis of phase transitions following the model developed in [54] for the case of the electroweak transition. …”

Section: Mass Of the Higgsmentioning

confidence: 99%

Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. Part I.

Chamseddine

Connes

2010

Fortschritte der Physik

132

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We examine the hypothesis that space-time is a product of a continuous four-dimensional manifold times a finite space. A new tensorial notation is developed to present the various constructs of noncommutative geometry. In particular, this notation is used to determine the spectral data of the standard model. The particle spectrum with all of its symmetries is derived, almost uniquely, under the assumption of irreducibility and of dimension 6 modulo 8 for the finite space. The reduction from the natural symmetry group SU (2) × SU (2) × SU (4) to U (1) × SU (2) × SU (3) is a consequence of the hypothesis that the two layers of space-time are finite distance apart but is non-dynamical. The square of the Dirac operator, and all geometrical invariants that appear in the calculation of the heat kernel expansion are evaluated. We re-derive the leading order terms in the spectral action. The geometrical action yields unification of all fundamental interactions including gravity at very high energies. We make the following predictions: (i) The number of fermions per family is 16. There is a right-handed neutrino with a see-saw mechanism. Moreover, the zeroth order spectral action obtained with a cut-off function is consistent with experimental data up to few percent. We discuss a number of open issues. We prepare the ground for computing higher order corrections since the predicted mass of the Higgs field is quite sensitive to the higher order corrections. We speculate on the nature of the noncommutative space at Planckian energies and the possible role of the fundamental group for the problem of generations.

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“…Thus, the spectral action at the unification scale Λ is directly applicable to early universe cosmological models [5][6][7][8], while extrapolations to lower energies can be obtained via RGE and inclusion of nonperturbative effects in the spectral action.…”

Section: Introductionmentioning

confidence: 99%

“…, is the topological term that integrates to the Euler characteristic, hence nondynamical, and the last one couples gravity to the Higgs field 1 and can have important consequences at high energies, such as in the early universe [5][6][7][8]. Here, we will be concerned with the low energy, weak curvature regime where this term is small.…”

Section: Introductionmentioning

confidence: 99%

Constraining the Noncommutative Spectral Action via Astrophysical Observations

2010

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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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Early universe models from noncommutative geometry

Cited by 46 publications

References 47 publications

Spectral action for Bianchi type-IX cosmological models

Spectral action for Bianchi type-IX cosmological models

Noncommutative geometry as a framework for unification of all fundamental interactions including gravity. Part I.

Constraining the Noncommutative Spectral Action via Astrophysical Observations

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