Skip to main content
SpringerLink
Log in

de Sitter Tachyons and Related Topics

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

We present a complete study of a family of tachyonic scalar fields living on the de Sitter universe. We show that for an infinite set of discrete values of the negative squared mass, the fields exhibit a gauge symmetry and there exists for them a fully acceptable local and covariant quantization similar to the Feynman–Gupta–Bleuler quantization of free QED. For general negative squares masses we also construct positive quantization where the de Sitter symmetry is spontaneously broken. We discuss the sense in which the two quantizations may be considered physically inequivalent even when there is a Lorentz invariant subspace in the second one.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bros, J., Epstein, H., Moschella, U.: Scalar tachyons in the de Sitter universe. Lett. Math. Phys. 93, 203 (2010). arXiv:1003.1396 [hep-th]

  2. Börner G., Dürr H.P.: Classical and quantum fields in de Sitter space. Il Nuovo Cimento A LXIV, 669–714 (1969)

    Article  Google Scholar 

  3. Allen B., Folacci A.: The massless minimally coupled scalar field in de Sitter space. Phys. Rev. D 35, 3771 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  4. Vilenkin A., Ford L.H.: Gravitational effects upon cosmological phase transition. Phys. Rev. D 26, 1231 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  5. Starobinsky A.A.: Dynamics of phase transition in the new inflationary universe scenario and generation of perturbations. Phys. Lett. 117, 175 (1982)

    Article  Google Scholar 

  6. Mazur P., Mottola E.: Spontaneous breaking of de Sitter symmetry by radiative effects. Nucl. Phys. B 278, 694 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  7. Antoniadis I., Mottola E.: Graviton fluctuations in de Sitter space. J. Math. Phys. 32, 1037 (1991)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  8. Antoniadis I., Mottola E.: 4-D quantum gravity in the conformal sector. Phys. Rev. D 45, 2013 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  9. Folacci A.: Toy model for the zero mode problem in the conformal sector of de Sitter quantum gravity. Phys. Rev. D 53, 3108 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  10. Folacci A.: Zero modes, euclideanization and quantization. Phys. Rev. D 46, 2553 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  11. Higuchi, A., Marolf, D., Morrison, I.A.: de Sitter invariance of the dS graviton vacuum. Class. Quant. Grav. 28, 245012 (2011). arXiv:1107.2712 [hep-th]]

  12. Faizal, M., Higuchi, A.: Physical equivalence between the covariant and physical graviton two-point functions in de Sitter spacetime. Phys. Rev. D 85, 124021 (2012). arXiv:1107.0395 [gr-qc]

  13. Mora P.J., Tsamis N.C., Woodard R.P.: Graviton propagator in a general invariant Gauge on de Sitter. J. Math. Phys. 53, 122502 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  14. Morrison, I.A.: On cosmic hair and “de Sitter breaking” in linearized quantum gravity. arXiv:1302.1860 [gr-qc]

  15. Miao, S.P., Mora, P.J., Tsamis, N.C., Woodard, R.P.: The perils of analytic continuation. Phys. Rev. D. 89, 104004 (2014). arXiv:1306.5410 [gr-qc]

  16. Miao, S.P., Tsamis, N.C., Woodard, R.P.: De Sitter breaking through infrared divergences. J. Math. Phys. 51, 072503 (2010). arXiv:1002.4037 [gr-qc]

  17. Streater R.F., Wightman A.S.: PCT, spin and statistics and all that. Princeton University Press, Princeton (1964)

    MATH  Google Scholar 

  18. Reed M., Simon B.: Methods of Modern Mathematical Physics, vol. 2. Academic Press, New York (1975)

    Google Scholar 

  19. Strocchi, F., Wightman, A.S.: Proof of the charge superselection rule in local relativistic quantum field theory. J. Math. Phys. 15, 2198 (1974) [Erratum ibid., 17, 1930 (1976)]

  20. Strocchi F.: Selected topics on the general properties of quantum field theory. World Sci. Lect. Notes Phys. 51, 1 (1993)

    Article  Google Scholar 

  21. Schroer B.: The quantization of m 2 < 0 field equations. Phys. Rev. D 3, 1764 (1971)

    Article  ADS  Google Scholar 

  22. Anderson, P.R., Eaker, W., Habib, S., Molina-Paris, C., Mottola, E.: Attractor states and infrared scaling in de Sitter space. Phys. Rev. D 62, 124019 (2000). arXiv:gr-qc/0005102

  23. Youssef, A.: Do scale-invariant fluctuations imply the breaking of de Sitter invariance? Phys. Lett. B 718, 1095 (2013). arXiv:1203.3171 [gr-qc]

  24. Feinberg G.: Possibility of faster-than-light particles. Phys. Rev. 159, 5 (1967)

    Article  Google Scholar 

  25. Bros J., Gazeau J.P., Moschella U.: Quantum field theory in the de Sitter universe. Phys. Rev. Lett. 73, 1746 (1994)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  26. Deser, S., Waldron, A.: Partial masslessness of higher spins in (A)dS. Nucl. Phys. B 607, 577 (2001). arXiv:hep-th/0103198

  27. Deser, S., Waldron, A.: Arbitrary spin representations in de Sitter from dS/CFT with applications to dS supergravity. Nucl. Phys. B 662, 379 (2003). arXiv:hep-th/0301068

  28. Bros, J., Moschella, U.: Two point functions and quantum fields in de Sitter universe. Rev. Math. Phys. 8, 327 (1996). arXiv:gr-qc/9511019

  29. Bros, J., Epstein, H., Moschella, U.: Analyticity properties and thermal effects for general quantum field theory on de Sitter space-time. Commun. Math. Phys. 196, 535 (1998). arXiv:gr-qc/9801099

  30. Faraut J.: Noyaux sphériques sur un hyperboloïde à une nappe in Lect Notes in Mathematics, vol. 497. Springer, Berlin (1975)

    Google Scholar 

  31. Molčanov V.F.: Harmonic analysis on a hyperboloid of one sheet. Soviet. Math. Dokl. 7, 1553–1556 (1966)

    Google Scholar 

  32. Thirring W.: Quantum field theory in de Sitter space. Acta Phys. Aust. Suppl. IV, 269 (1967)

    Google Scholar 

  33. Nachtmann O.: Dynamische Stabilität im de-Sitter-raum. Österr. Akad. Wiss. Math.-Naturw. Kl. Abt. II 176, 363–379 (1968)

    MATH  Google Scholar 

  34. Chernikov N.A., Tagirov E.A.: Quantum theory of scalar fields in de Sitter space-time. Ann. Poincare. Phys. Theor. A 9, 109 (1968)

    MATH  MathSciNet  Google Scholar 

  35. Schomblond C., Spindel P.: Conditions d’unicité pour le propagateur Δ1(x, y) du champ scalaire dans l’univers de de Sitter. Ann. Poincare Phys. Theor. 25, 67 (1976)

    ADS  MATH  MathSciNet  Google Scholar 

  36. Gibbons G.W., Hawking S.W.: Cosmological event horizons, thermodynamics, and particle creation. Phys. Rev. D 15, 2738–2751 (1977)

    Article  ADS  MathSciNet  Google Scholar 

  37. Bunch T.S., Davies P.C.W.: Quantum field theory in de Sitter space: renormalization by point splitting. Proc. R. Soc. Lond. A 360, 117 (1978)

  38. Mottola E.: Particle creation in de Sitter space. Phys. Rev. D. 31, 754 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  39. Allen B.: Vacuum states in de Sitter space. Phys. Rev. D 32, 3136 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  40. Erdélyi A.: The Bateman Manuscript Project Higher Transcendental Functions, vol. II. McGraw-Hill, New York (1953)

    Google Scholar 

  41. Vilenkin N.Ja.: Special Functions and the Theory of Group Representations. Nauka, Moscow (1968)

    MATH  Google Scholar 

  42. Erdélyi A.: The Bateman Manuscript Project Higher Transcendental Functions, vol. I. McGraw-Hill, New York (1953)

    Google Scholar 

  43. Dimock J.: Algebras of local observables on a manifold. Commun. Math. Phys. 77, 211–297 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  44. Wald R.M.: Quantum Field Theory in Curved Space-Time and Black Hole Thermodynamics. Chicago University Press, Chicago (1995)

    Google Scholar 

  45. Moschella U., Schaeffer R.: Quantum fields on curved spacetimes and a new look at the Unruh effect. AIP Conf. Proc. 1132, 303–332 (2009)

    Article  ADS  Google Scholar 

  46. Miao, S.P., Tsamis, N.C., Woodard, R.P.: The graviton propagator in de Donder Gauge on de Sitter background. J. Math. Phys. 52, 122301 (2011). arXiv:1106.0925 [gr-qc]

  47. Gelfand I.M., Graev M.I., Vilenkin N.Ya.: Generalized Functions, vol. 5. Integral Geometry and Representation Theory. Academic Press, Boston (1966)

    Google Scholar 

  48. Bros J., Moschella U.: Fourier analysis and holomorphic decomposition on the one sheeted hyperboloid, arXiv:math-ph/0311052. In: Norguet, F., Ofman, S., Szczeciniarz, J.-J. (eds) Géométrie complexe II., pp. 100–145. Hermann, Paris (2003)

  49. Polyakov, A.M.: De Sitter space and eternity. Nucl. Phys. B 797, 199 (2008). arXiv:0709.2899 [hep-th]

  50. Polyakov, A.M.: Infrared instability of the de Sitter space. arXiv:1209.4135 [hep-th]

  51. Anderson, P.R., Mottola, E.: Quantum vacuum instability of ‘Eternal’ de Sitter space. Phys. Rev. D. 89, 104039 (2014). arXiv:1310.1963 [gr-qc]

  52. Anderson, P.R., Mottola, E.: On the instability of global de Sitter space to particle creation. Phys. Rev. D, 104038 (2014). arXiv:1310.0030 [gr-qc]

  53. Akhmedov, E.T.: Lecture notes on interacting quantum fields in de Sitter space. Int. J. Mod. Phys. D 23, 1430001 (2014). arXiv:1309.2557 [hep-th]

  54. Morchio G., Strocchi F.: Infrared singularities, vacuum structure and pure phases in local quantum field theory. Annales de l’institut Henri Poincaré (A) Physique théorique 33(3), 251–282 (1980)

    MathSciNet  Google Scholar 

  55. Morchio G., Pierotti D., Strocchi F.: Infrared and vacuum structure in two-dimensional local quantum field theory models. The massless scalar field. J. Math. Phys. 31, 1467 (1990)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  56. Bertola, M., Corbetta, F., Moschella, U. (2007). Massless scalar field in two-dimensional de Sitter universe. Prog. Math. 251, 27 arXiv:math-ph/0609080

  57. Hawking S.W., Ellis G.F.R.: The Large Scale Structure of Space-Time. Cambridge University Press, Cambridge (1973)

    Book  MATH  Google Scholar 

  58. Mehta M.: Matrix Theory. Les Editions de Physique, Les Ulis (1989)

    Google Scholar 

  59. Szegö, G.: Orthogonal Polynomials. American Mathematical Society, Providence (1975)

Download references

Author information

Authors and Affiliations

  1. Institut des Hautes Études Scientifiques, 91440, Bures-sur-Yvette, France

    Henri Epstein & Ugo Moschella

  2. DiSat, Università dell’Insubria, 22100, Como, Italy

    Ugo Moschella

  3. INFN, Sez. di Milano, Milan, Italy

    Ugo Moschella

Authors
  1. Henri Epstein
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ugo Moschella
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Henri Epstein.

Additional information

Communicated by A. Connes

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Epstein, H., Moschella, U. de Sitter Tachyons and Related Topics. Commun. Math. Phys. 336, 381–430 (2015). https://doi.org/10.1007/s00220-015-2308-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00220-015-2308-x

Keywords

Search

Navigation