Causal structures in inflation

George F.R. Ellis; Jean-Philippe Uzan

doi:10.1016/j.crhy.2015.07.005

Causal structures in inflation

George F.R. Ellis ¹; Jean-Philippe Uzan ^2,³

¹ Mathematics and Applied Mathematics Department, University of Cape Town, Rondebosch, Cape Town 7701, South Africa
² Institut d'astrophysique de Paris, UMR 7095 du CNRS, Université Pierre-et-Marie-Curie, 98 bis, boulevard Arago, 75014 Paris, France
³ Sorbonne Universités, Institut Lagrange de Paris, 98 bis, boulevard Arago, 75014 Paris, France

Comptes Rendus. Physique, Cosmic inflation / Inflation cosmique, Volume 16 (2015) no. 10, pp. 928-947.

Abstract
Résumé

This article reviews the properties and limitations associated with the existence of particle, visual, and event horizons in cosmology in general and in inflationary universes in particular, carefully distinguishing them from ‘Hubble horizons’. It explores to what extent one might be able to probe conditions beyond the visual horizon (which is close in size to the present Hubble radius), thereby showing that visual horizons place major limits on what are observationally testable aspects of a multiverse, if such exists. Indeed these limits largely prevent us from observationally proving a multiverse either does or does not exist. We emphasize that event horizons play no role at all in observational cosmology, even in the multiverse context, despite some claims to the contrary in the literature.

Cet article définit, puis passe en revue les propriétés et les limites associées à l'existence d'horizons (des particules, des événements et visuels) en cosmologie en général et pendant l'inflation en particulier, en insistant sur leurs différences avec les « horizons de Hubble ». Il discute la possibilité de tester les conditions physiques de l'univers au-delà de notre horizon visuel (qui, en taille, est proche du rayon de Hubble) et démontre que l'existence d'horizons visuels impose des limites strictes sur ce qui est potentiellement testable dans les scénarios de type multivers, s'ils existent. Ces limites nous interdisent de prouver observationnellement l'existence ou la non-existence de ces multivers. Il est aussi démontré que les horizons des événements ne jouent aucun rôle en cosmologie observationnelle, même dans le contexte des modèles de multivers.

Published online: 2015-09-02

DOI: 10.1016/j.crhy.2015.07.005

Keywords: Cosmology, Inflation, Causal structures
Mots-clés : Cosmologie, Inflation, Structures causales

Author's affiliations:

George F.R. Ellis ¹; Jean-Philippe Uzan ^{2, 3}

¹ Mathematics and Applied Mathematics Department, University of Cape Town, Rondebosch, Cape Town 7701, South Africa
² Institut d'astrophysique de Paris, UMR 7095 du CNRS, Université Pierre-et-Marie-Curie, 98 bis, boulevard Arago, 75014 Paris, France
³ Sorbonne Universités, Institut Lagrange de Paris, 98 bis, boulevard Arago, 75014 Paris, France

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     title = {Causal structures in inflation},
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     pages = {928--947},
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     number = {10},
     year = {2015},
     doi = {10.1016/j.crhy.2015.07.005},
     language = {en},
}

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George F.R. Ellis; Jean-Philippe Uzan. Causal structures in inflation. Comptes Rendus. Physique, Cosmic inflation / Inflation cosmique, Volume 16 (2015) no. 10, pp. 928-947. doi : 10.1016/j.crhy.2015.07.005. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2015.07.005/

References
Cited by

[1] R. Penrose Relativity, Groups and Topology, 43 (1964), p. 565 (Reprinted in Gen. Relativ. Gravit., 2011, pp. 901)

[2] W. Rindler Mon. Not. R. Astron. Soc., 116 (1956), p. 662 (Reprinted in Gen. Relativ. Gravit., 34, 2002, pp. 133)

[3] S.W. Hawking; G.F.R. Ellis The Large Scale Structure of Spacetime, Cambridge University Press, Cambridge, 1973

[4] F.J. Tipler et al. General Relativity and Gravitation: One Hundred Years After the Birth of Albert Einstein, vol. 2 (A. Held, ed.), Plenum Press, New York, NY, 1980, p. 97

[5] P. Peter; J.-P. Uzan Primordial Cosmology, Oxford University Press, Oxford, 2009

[6] N. Deruelle; J.-P. Uzan Théories de la relativité, Belin, Paris, 2014

[7] J. Ehlers Akad. Wiss. Lit. Mainz, Abhandl. Math.-Nat. Kl., 11 (1961), pp. 793-837 (Reprinted in Gen. Relativ. Gravit., 25, 1993, pp. 1225-1266)

[8] G.F.R. Ellis General Relativity and Cosmology, 41 (1971), pp. 565-660 (Reprinted in Gen. Relativ. Gravit., 2009, pp. 581)

[9] A. Sandage; G. McVittie; J.-P. Uzan; F. Bernardeau; Y. Mellier Phys. Rev. D, 136 (1962), p. 319

[10] R. Wald Gravitation, University of Chicago Press, 2010

[11] G.F.R. Ellis; W. Stoeger Class. Quantum Gravity, 5 (1988), p. 207

[12] G.F.R. Ellis; T. Rothman Am. J. Phys., 61 (1993), p. 883

[13] G.F.R. Ellis; G. Schreiber; J.-P. Luminet; et al.; N.J. Cornish; et al.; A. Riazuelo; et al.; J.-P. Uzan et al. Phys. Rev. D, 115, 1986, p. 97 | arXiv

[14] J.A. Wolf; M. Lachièze-Rey; J.-P. Luminet; J.-P. Uzan Int. J. Theor. Phys., 254 (1967), p. 135

[15] V.F. Mukhanov; H.A. Feldman; R.H. Brandenberger Theory of cosmological perturbations, Phys. Rep., Volume 215 (1992), p. 203

[16] R. Penrose Phys. Rev. Lett., 14 (1965), p. 57

[17] R. Penrose Les Houches 1963 (C. de Witt; B. de Witt, eds.), Gordon and Breach (1964), p. 561

[18] J.T. Firouzjaee; G.F.R. Ellis | arXiv

[19] S. Winitzki Phys. Rev. D, 71 (2005)

[20] T.M. Davis; C.H. Lineweaver | arXiv

[21] T.M. Davis; C.H. Lineweaver | arXiv

[22] H. Lee; S.-C. Su; D. Baumann; D. Baumann; M. Zaldarriaga J. Cosmol. Astropart. Phys., 0906 (2009) | arXiv

[23] O. Fabre; S. Prunet; J.-P. Uzan | arXiv

[24] L. Kofman Les Houches 2006 (F. Bernardeau et al., eds.), Elsevier (2007), p. 195

[25] G. Gibbons; S. Hawking; T. Bunch; P. Davies Proc. R. Soc. A, 15 (1977), p. 2738

[26] L. Susskind | arXiv

[27] A. Starobinsky; V. Mukhanov; G. Chibisov; A. Vilenkin; L. Ford; A. Linde Phys. Lett. B, 117 (1982), p. 175

[28] N.J. Cornish; D.N. Spergel; G.D. Starkman Phys. Rev. Lett., 77 (1996), p. 215

[29] B. Freivogel; M. Kleban; A. Nicolis; K. Sigurdson J. Cosmol. Astropart. Phys., 0908 (2009)

[30] B. Freivogel; M. Kleban; M.R. Martinez; L. Susskind | arXiv

[31] M. Kleban; S. Chang; M. Kleban; T.S. Levi J. Cosmol. Astropart. Phys., 28 (2011), p. 204008

[32] G.F.R. Ellis; W. Stoeger Gen. Relativ. Gravit., 41 (2009), p. 1475

[33] L. Susskind The Cosmic Landscape: String Theory and the Illusion of Intelligent Design, Little, Brown, New York, 2005

[34] G.F.R. Ellis Gen. Relativ. Gravit., 38 (2006), p. 1209

[35] V. Mukhanov Physical Foundations of Cosmology, Cambridge University Press, Cambridge, UK, 2005

[36] H. Lee; S.-C. Su; D. Baumann | arXiv

[37] L.M. Krauss; R.J. Scherrer Gen. Relativ. Gravit., 39 (2007), p. 1545

[38] E.W. Kolb et al. Mod. Phys. Lett. A, 20 (2005), p. 2705

[39] P. Zhang; A. Stebbins Phys. Rev. Lett., 107 (2011)

[40] W. Hu | arXiv

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