Comptes Rendus
Testing quantum gravity with cosmology/Tester les théories de la gravitation quantique à l'aide de la cosmologie
Spectral action gravity and cosmological models
[Action spectrale, gravitation et modèles cosmologiques]
Comptes Rendus. Physique, Volume 18 (2017) no. 3-4, pp. 226-234.

Cet article passe en revue les travaux récents de l'auteure et de ses collaborateurs sur les modèles cosmologiques basés sur la fonctionnelle d'action spectrale de la gravitation. Une présentation plus détaillée des sujets abordés ici sera proposée dans un livre à venir [1].

This paper surveys recent work of the author and collaborators on cosmological models based on the spectral action functional of gravity. A more detailed presentation of the topics surveyed here will be available in a forthcoming book [1].

Publié le :
DOI : 10.1016/j.crhy.2017.03.001
Keywords: Modified gravity, Spectral action, Dirac operator, Cosmic inflation
Mot clés : Gravité modifiée, Action spectrale, Opérateur de Dirac, Inflation cosmique
Matilde Marcolli 1

1 Division of Physics, Mathematics, and Astronomy, California Institute of Technology, 1200 E. California Blvd, Pasadena, CA 91125, USA
@article{CRPHYS_2017__18_3-4_226_0,
     author = {Matilde Marcolli},
     title = {Spectral action gravity and cosmological models},
     journal = {Comptes Rendus. Physique},
     pages = {226--234},
     publisher = {Elsevier},
     volume = {18},
     number = {3-4},
     year = {2017},
     doi = {10.1016/j.crhy.2017.03.001},
     language = {en},
}
TY  - JOUR
AU  - Matilde Marcolli
TI  - Spectral action gravity and cosmological models
JO  - Comptes Rendus. Physique
PY  - 2017
SP  - 226
EP  - 234
VL  - 18
IS  - 3-4
PB  - Elsevier
DO  - 10.1016/j.crhy.2017.03.001
LA  - en
ID  - CRPHYS_2017__18_3-4_226_0
ER  - 
%0 Journal Article
%A Matilde Marcolli
%T Spectral action gravity and cosmological models
%J Comptes Rendus. Physique
%D 2017
%P 226-234
%V 18
%N 3-4
%I Elsevier
%R 10.1016/j.crhy.2017.03.001
%G en
%F CRPHYS_2017__18_3-4_226_0
Matilde Marcolli. Spectral action gravity and cosmological models. Comptes Rendus. Physique, Volume 18 (2017) no. 3-4, pp. 226-234. doi : 10.1016/j.crhy.2017.03.001. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2017.03.001/

[1] M. Marcolli Noncommutative Cosmology, World Scientific, September 2017 (in press) (ISBN: 978-981-3202-83-2)

[2] T. Clifton; P.G. Ferreira; A. Padilla; C. Skordis Modified gravity and cosmology, Phys. Rep., Volume 513 (2012) no. 1, pp. 1-189

[3] K. Koyama Cosmological tests of modified gravity, Rep. Prog. Phys., Volume 79 (2016) no. 4

[4] A. Chamseddine; A. Connes The spectral action principle, Commun. Math. Phys., Volume 186 (1997) no. 3, pp. 731-750

[5] A. Chamseddine; A. Connes; M. Marcolli Gravity and the standard model with neutrino mixing, Adv. Theor. Math. Phys., Volume 11 (2007), pp. 991-1090

[6] A.H. Chamseddine; A. Connes Resilience of the spectral standard model, J. High Energy Phys., Volume 1209 (2012)

[7] C. Estrada; M. Marcolli Asymptotic safety, hypergeometric functions, and the Higgs mass in spectral action models, Int. J. Geom. Methods Mod. Phys., Volume 10 (2013) no. 7, p. 1350036

[8] W. Beenakker; T. van den Broek; W.D. van Suijlekom Supersymmetry and Noncommutative Geometry, Springer Briefs in Mathematical Physics, 2015

[9] A.H. Chamseddine; A. Connes; W. van Suijlekom Beyond the spectral standard model: emergence of Pati–Salam unification, J. High Energy Phys., Volume 1311 (2013)

[10] D. Kastler The Dirac operator and gravitation, Commun. Math. Phys., Volume 166 (1995) no. 3, pp. 633-643

[11] A. Chamseddine; A. Connes The uncanny precision of the spectral action, Commun. Math. Phys., Volume 293 (2010) no. 3, pp. 867-897

[12] P.D. Mannheim Making the case for conformal gravity, Found. Phys., Volume 42 (2012) no. 3, pp. 388-420

[13] W. Nelson; J. Ochoa; M. Sakellariadou Constraining the noncommutative spectral action via astrophysical observations, Phys. Rev. Lett., Volume 105 (2010)

[14] W. Nelson; J. Ochoa; M. Sakellariadou Gravitational waves in the spectral action of noncommutative geometry, Phys. Rev. D, Volume 82 (2010)

[15] A. Connes; M. Marcolli Noncommutative Geometry, Quantum Fields, and Motives, Colloq. Publ., vol. 55, American Mathematical Society, 2008

[16] H. Arason; D.J. Castano; B. Kesthlyi; E.J. Piard; P. Ramond; B.D. Wright Renormalization-group study of the standard model and its extensions: the standard model, Phys. Rev. D, Volume 46 (1992) no. 9, pp. 3945-3965

[17] I.G. Avramidi Covariant Methods for the Calculation of the Effective Action in Quantum Field Theory and Investigation of Higher-Derivative Quantum Gravity, Moscow University, 1986 (PhD Thesis) | arXiv

[18] A. Codello; R. Percacci Fixed points of higher derivative gravity, Phys. Rev. Lett., Volume 97 (2006)

[19] J.F. Donoghue General relativity as an effective field theory: the leading quantum corrections, Phys. Rev. D, Volume 50 (1994) no. 6, pp. 3874-3888

[20] D. Kolodrubetz; M. Marcolli Boundary conditions of the RGE flow in the noncommutative geometry approach to particle physics and cosmology, Phys. Lett. B, Volume 693 (2010), pp. 166-174

[21] S. Antusch; J. Kersten; M. Lindner; M. Ratz; M.A. Schmidt Running neutrino mass parameters in see-saw scenarios, J. High Energy Phys., Volume 03 (2005)

[22] M. Marcolli; E. Pierpaoli Early universe models from noncommutative geometry, Adv. Theor. Math. Phys., Volume 14 (2010), pp. 1373-1432

[23] I.D. Novikov; A.G. Polnarev; A.A. Starobinsky; Ya.B. Zeldovich Primordial black holes, Astron. Astrophys., Volume 80 (1979), pp. 104-109

[24] J.D. Barrow Gravitational memory?, Phys. Rev. D, Volume 46 (1992) no. 8

[25] B.J. Carr Primordial black holes as a probe of the early universe and a varying gravitational constant | arXiv

[26] A.A. Belyanin; V.V. Kocharovsky; V.I.V. Kocharovsky Gamma-ray bursts from evaporating primordial black holes, Radiophys. Quantum Electron., Volume 41 (1996) no. 1, pp. 22-27

[27] A.D. Linde Gauge theories, time-dependence of the gravitational constant and antigravity in the early universe, Phys. Lett. B, Volume 93 (1980) no. 4, pp. 394-396

[28] M.V. Safonova; D. Lohiya Gravity balls in induced gravity models – ‘gravitational lens’ effects, Gravit. Cosmol. (1998) no. 1, pp. 1-10

[29] F. Hoyle; J.V. Narlikar A new theory of gravitation, Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci., Volume 282 (1964) no. 1389, pp. 191-207

[30] J.M. Overduin; F.I. Cooperstock Evolution of the scale factor with a variable cosmological term, Phys. Rev. D, Volume 58 (1998)

[31] A. De Simone; M.P. Hertzberg; F. Wilczek Running inflation in the standard model, Phys. Lett. B, Volume 678 (2009) no. 1, pp. 1-8

[32] M. Buck; M. Fairbairn; M. Sakellariadou Inflation in models with conformally coupled scalar fields: an application to the noncommutative spectral action, Phys. Rev. D, Volume 82 (2010)

[33] W. Nelson; M. Sakellariadou Inflation mechanism in asymptotic noncommutative geometry, Phys. Lett. B, Volume 680 (2009), pp. 263-266

[34] M. Lachièze-Rey; J.P. Luminet Cosmic topology, Phys. Rep., Volume 254 (1995), pp. 135-214

[35] S. Caillerie; M. Lachièze-Rey; J.P. Luminet; R. Lehoucq; A. Riazuelo; J. Weeks A new analysis of the Poincaré dodecahedral space model, Astron. Astrophys., Volume 476 (2007) no. 2, pp. 691-696

[36] N.J. Cornish; D.N. Spergel; G.D. Starkman; E. Komatsu Constraining the topology of the universe, Phys. Rev. Lett., Volume 92 (2004)

[37] E. Gausmann; R. Lehoucq; J.P. Luminet; J.P. Uzan; J. Weeks Topological lensing in spherical spaces, Class. Quantum Gravity, Volume 18 (2001), pp. 5155-5186

[38] G.I. Gomero; M.J. Reboucas; R. Tavakol Detectability of cosmic topology in almost flat universes, Class. Quantum Gravity, Volume 18 (2001), pp. 4461-4476

[39] J.P. Luminet; J. Weeks; A. Riazuelo; R. Lehoucq Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background, Nature, Volume 425 (2003), pp. 593-595

[40] A. Riazuelo; J.P. Uzan; R. Lehoucq; J. Weeks Simulating cosmic microwave background maps in multi-connected spaces, Phys. Rev. D, Volume 69 (2004)

[41] A. Moss; D. Scott; J.P. Zibin No evidence for anomalously low variance circles on the sky | arXiv

[42] I.K. Wehus; H.K. Eriksen A search for concentric circles in the 7-year WMAP temperature sky maps, Astrophys. J. Lett., Volume 733 (2011) no. 2

[43] M. Marcolli; E. Pierpaoli; K. Teh The spectral action and cosmic topology, Commun. Math. Phys., Volume 304 (2011) no. 1, pp. 125-174

[44] M. Marcolli; E. Pierpaoli; K. Teh The coupling of topology and inflation in noncommutative cosmology, Commun. Math. Phys., Volume 309 (2012) no. 2, pp. 341-369

[45] B. Ćaćić; M. Marcolli; K. Teh Coupling of gravity to matter, spectral action and cosmic topology, J. Noncommut. Geom., Volume 8 (2014) no. 2, pp. 473-504

[46] K. Teh Nonperturbative spectral action of round coset spaces of SU(2), J. Noncommut. Geom., Volume 7 (2013) no. 3, pp. 677-708

[47] C. Bär The Dirac operator on space forms of positive curvature, J. Math. Soc. Jpn., Volume 48 (1996) no. 1, pp. 69-83

[48] J. Cisneros-Molina The η-invariant of twisted Dirac operators of S3/Γ, Geom. Dedic., Volume 84 (2001), pp. 207-228

[49] N. Ginoux The Dirac Spectrum, Lect. Notes Math., vol. 1976, Springer, 2009

[50] M. Kamionkowski; D.N. Spergel; N. Sugiyama Small-scale cosmic microwave background anisotropies as a probe of the geometry of the universe, Astrophys. J., Volume 426 (1994)

[51] J.E. Lidsey; A.R. Liddle; E.W. Kolb; E.J. Copeland; T. Barreiro; M. Abney Reconstructing the inflaton potential – an overview, Rev. Mod. Phys., Volume 69 (1997), pp. 373-410

[52] T.L. Smith; M. Kamionkowski; A. Cooray Direct detection of the inflationary gravitational wave background, Phys. Rev. D, Volume 73 (2006) no. 2

[53] M. Dahl Prescribing eigenvalues of the Dirac operator, Manuscr. Math., Volume 118 (2005), pp. 191-199

[54] M. Dahl Dirac eigenvalues for generic metrics on three-manifolds, Ann. Glob. Anal. Geom., Volume 24 (2003), pp. 95-100

[55] S. Farnsworth; L. Boyle Rethinking Connes' approach to the standard model of particle physics via non-commutative geometry, New J. Phys., Volume 17 ( February 2015 )

[56] D.I. Kaiser; E.I. Sfakianakis Multifield inflation after Planck: the case for nonminimal couplings, Phys. Rev. Lett., Volume 112 (2014)

[57] A.H. Chamseddine; A. Connes Spectral action for Robertson–Walker metrics, J. High Energy Phys. (2012) no. 10

[58] F. Fathizadeh; A. Ghorbanpour; M. Khalkhali Rationality of spectral action for Robertson–Walker metrics, J. High Energy Phys. (2014) no. 12

[59] W. Fan; F. Fathizadeh; M. Marcolli Spectral action for Bianchi type-IX cosmological models, J. High Energy Phys. (2015)

[60] F. Fathizadeh; M. Marcolli Periods and motives in the spectral action of Robertson–Walker spacetimes | arXiv

[61] M. Kontsevich; D. Zagier Periods, Mathematics Unlimited – 2001 and Beyond, Springer, 2001, pp. 771-808

[62] V. Voevodsky Triangulated categories of motives over a field, Cycles, Transfers, and Motivic Homology Theories, Ann. Math. Stud., vol. 143, Princeton University Press, 2000, pp. 188-238

[63] M. Marcolli Feynman Motives, World Scientific, 2010

[64] W. Fan; F. Fathizadeh; M. Marcolli Modular forms in the spectral action of Bianchi IX gravitational instantons | arXiv

[65] M.V. Babich; D.A. Korotkin Self-dual SU(2)-invariant Einstein metrics and modular dependence of theta-functions, Lett. Math. Phys., Volume 46 (1998), pp. 323-337

[66] K.P. Tod Self-dual Einstein metrics from the Painlevé VI equation, Phys. Lett. A, Volume 190 (1994), pp. 221-224

[67] Yu.I. Manin; M. Marcolli Big Bang, blowup, and modular curves: algebraic geometry in cosmology, SIGMA, Volume 10 (2014)

[68] Yu.I. Manin; M. Marcolli Symbolic dynamics, modular curves, and Bianchi IX cosmologies, Ann. Fac. Sci. Toulouse, Volume XXV (2016) no. 2–3, pp. 313-338

[69] Quantum Cosmology (L.Z. Fang; R. Ruffini, eds.), World Scientific, 1987

[70] I.M. Khalatnikov; E.M. Lifshitz; K.M. Khanin; L.N. Shchur; Ya.G. Sinai On the stochasticity in relativistic cosmology, J. Stat. Phys., Volume 38 (1985) no. 1/2, pp. 97-114

[71] C. Estrada; M. Marcolli Noncommutative mixmaster cosmologies, Int. J. Geom. Methods Mod. Phys., Volume 10 (2013) no. 1, p. 1250086

[72] D.H. Mayer Relaxation properties of the mixmaster universe, Phys. Lett. A, Volume 121 (1987) no. 8, 9, pp. 390-394

[73] Yu.I. Manin; M. Marcolli Continued fractions, modular symbols, and noncommutative geometry, Selecta Math. (N.S.), Volume 8 (2002) no. 3, pp. 475-521

[74] M. Marcolli Modular curves, C-algebras, and chaotic cosmology, Frontiers in Number Theory, Physics, and Geometry. II, Springer, 2007, pp. 361-372

[75] M. Marcolli Arithmetic Noncommutative Geometry, Univ. Lect. Ser., vol. 36, American Mathematical Society, 2005

[76] M.J. Rees; D.W. Sciama Large-scale density inhomogeneities in the universe, Nature, Volume 217 (1968), pp. 511-516

[77] J.R. Mureika; C.C. Dyer Multifractal analysis of packed swiss cheese cosmologies, Gen. Relativ. Gravit., Volume 36 (2004) no. 1, pp. 151-184

[78] F. Sylos Labini; M. Montuori; L. Pietroneo Scale-invariance of galaxy clustering, Phys. Rep., Volume 293 (1998) no. 2–4, pp. 61-226

[79] A. Ball; M. Marcolli Spectral action models of gravity on packed swiss cheese cosmology, Class. Quantum Gravity, Volume 33 (2016), p. 115018

[80] E. Christensen; C. Ivan; M.L. Lapidus Dirac operators and spectral triples for some fractal sets built on curves, Adv. Math., Volume 217 (2008) no. 1, pp. 42-78

[81] R.L. Graham; J.C. Lagarias; C.L. Mallows; A.R. Wilks; C.H. Yan Apollonian circle packings: geometry and group theory III. Higher dimensions, Discrete Comput. Geom., Volume 35 (2006), pp. 37-72

[82] M.L. Lapidus; M. van Frankenhuijsen Fractal Geometry, Complex Dimensions and Zeta Functions. Geometry and Spectra of Fractal Strings, Springer, 2013

[83] G.V. Dunne Heat kernels and zeta functions on fractals, J. Phys. A, Math. Theor., Volume 45 (2012) no. 37, p. 374016

Cité par Sources :

Commentaires - Politique


Ces articles pourraient vous intéresser

Testing different approaches to quantum gravity with cosmology: An overview

Aurélien Barrau

C. R. Phys (2017)


Isotropization of the universe during inflation

Thiago Pereira; Cyril Pitrou

C. R. Phys (2015)


Asymptotically safe cosmology – A status report

Alfio Bonanno; Frank Saueressig

C. R. Phys (2017)