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Covariant vacuum polarizations on de Sitter background

Katie E. Leonard1,*, T. Prokopec2,†, and R. P. Woodard1,‡

  • 1Department of Physics, University of Florida, Gainesville, Florida 32611, USA
  • 2Institute of Theoretical Physics (ITP) and Spinoza Institute, Utrecht University, Postbus 80195, 3508 TD Utrecht, The Netherlands

  • *katie@phys.ufl.edu
  • †T.Prokopec@uu.nl
  • ‡woodard@phys.ufl.edu
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Phys. Rev. D 87, 044030 – Published 15 February, 2013

DOI: https://doi.org/10.1103/PhysRevD.87.044030

Abstract

We derive covariant expressions for the one-loop vacuum polarization induced by a charged scalar on de Sitter background. Two forms are employed: one in which two covariant derivatives act on de Sitter-invariant basis tensors multiplied by scalar structure functions, and the other in which four covariant derivatives act on a single basis tensor times a structure function. The second representation permits the correction to dynamical photons to be expressed as a surface integral, which raises the important question of what sorts of effects can be absorbed into corrections of the initial state. Results are obtained for charged, minimally coupled scalars which are either massless or else light. The former show de Sitter breaking whereas the latter are de Sitter invariant. However, the de Sitter-invariant formulation does not seem useful, even when it is possible. Our work has two important physical consequences: (1) an upcoming computation of the vacuum polarization from inflationary gravitons should be expressed using the old, noncovariant formalism, and (2) one should re-examine the conclusion of a previous study of the effect of inflationary scalars on gravitons.

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References (38)

  1. T. Prokopec, O. Törnkvist, and R. P. Woodard, Phys. Rev. Lett. 89, 101301 (2002); Ann. Phys. (Amsterdam) 303, 251 (2003).
  2. T. Prokopec and E. Puchwein, J. Cosmol. Astropart. Phys. 04 (2004) 007.
  3. T. Prokopec and R. P. Woodard, Am. J. Phys. 72, 62 (2004); Ann. Phys. (Amsterdam) 312, 1 (2004).
  4. A. C. Davis, K. Dimopoulos, T. Prokopec, and O. Törnkvist, Phys. Lett. B 501, 165 (2001); K. Dimopoulos, T. Prokopec, O. Törnkvist, and A. C. Davis, Phys. Rev. D 65, 063505 (2002).
  5. N. C. Tsamis and R. P. Woodard, Commun. Math. Phys. 162, 217 (1994).
  6. R. P. Woodard, in Deserfest: A Celebration of the Life and Works of Stanley Deser, edited by J. T. Liu, M. J. Duff, K. S. Stelle, and R. P. Woodard (World Scientific, Hackensack, 2006), p. 339.
  7. S. P. Miao, N. C. Tsamis, and R. P. Woodard, Classical Quantum Gravity 28, 245013 (2011).
  8. A. Higuchi and Y. C. Lee, Phys. Rev. D 78, 084031 (2008); M. Faizal and A. Higuchi, 78, 067502 (2008); 85, 124021 (2012).
  9. A. Higuchi, D. Marolf, and I. A. Morrison, Classical Quantum Gravity 28, 245012 (2011).
  10. T. Prokopec, N. C. Tsamis, and R. P. Woodard, Classical Quantum Gravity 24, 201 (2007); Ann. Phys. (Amsterdam) 323, 1324 (2008); Phys. Rev. D 78, 043523 (2008).
  11. N. C. Tsamis and R. P. Woodard, J. Math. Phys. (N.Y.) 48, 052306 (2007).
  12. B. Allen and A. Folacci, Phys. Rev. D 35, 3771 (1987).
  13. E. O. Kahya and R. P. Woodard, Phys. Rev. D 72, 104001 (2005); 74, 084012 (2006).
  14. S. P. Miao, N. C. Tsamis, and R. P. Woodard, J. Math. Phys. (N.Y.) 51, 072503 (2010).
  15. V. K. Onemli and R. P. Woodard, Classical Quantum Gravity 19, 4607 (2002); Phys. Rev. D 70, 107301 (2004).
  16. S. P. Miao, N. C. Tsamis, and R. P. Woodard, J. Math. Phys. (N.Y.) 52, 122301 (2011).
  17. N. A. Chernikov and E. A. Tagirov, Ann. Poincare Phys. Theor. A 9, 109 (1968).
  18. J. Schwinger, J. Math. Phys. (N.Y.) 2, 407 (1961); K. T. Mahanthappa, Phys. Rev. 126, 329 (1962); P. M. Bakshi and K. T. Mahanthappa, J. Math. Phys. (N.Y.) 4, 1 (1963); 4, 12 (1963); L. V. Keldysh, Sov. Phys. JETP 20, 1018 (1965); K. C. Chou, Z. B. Su, B. L. Hao, and L. Yu, Phys. Rep. 118, 1 (1985); R. D. Jordan, Phys. Rev. D 33, 444 (1986); E. Calzetta and B. L. Hu, 35, 495 (1987).
  19. L. H. Ford and R. P. Woodard, Classical Quantum Gravity 22, 1637 (2005).
  20. T. Prokopec and R. P. Woodard, J. High Energy Phys. 10 (2003) 059; B. Garbrecht and T. Prokopec, Phys. Rev. D 73, 064036 (2006); S. P. Miao and R. P. Woodard, 74, 044019 (2006).
  21. T. Brunier, V. K. Onemli, and R. P. Woodard, Classical Quantum Gravity 22, 59 (2005); E. O. Kahya and V. K. Onemli, Phys. Rev. D 76, 043512 (2007).
  22. L. D. Duffy and R. P. Woodard, Phys. Rev. D 72, 024023 (2005).
  23. S. P. Miao and R. P. Woodard, Classical Quantum Gravity 23, 1721 (2006); Phys. Rev. D 74, 024021 (2006); Classical Quantum Gravity 25, 145009 (2008); S. P. Miao, Ph.D thesis, University of Florida [arXiv:0705.0767]; Phys. Rev. D 86, 104051 (2012).
  24. E. O. Kahya and R. P. Woodard, Phys. Rev. D 76, 124005 (2007); 77, 084012 (2008).
  25. S. Park and R. P. Woodard, Classical Quantum Gravity 27, 245008 (2010).
  26. S. Park and R. P. Woodard, Phys. Rev. D 83, 084049 (2011); 84, 124058 (2011).
  27. K. E. Leonard and R. P. Woodard, Phys. Rev. D 85, 104048 (2012).
  28. E. O. Kahya, V. K. Onemli, and R. P. Woodard, Phys. Rev. D 81, 023508 (2010).
  29. J. Z. Simon, Phys. Rev. D 41, 3720 (1990); 43, 3308 (1991).
  30. W. Pauli, Helv. Phys. Acta 4, 68 (1956); S. Deser, Rev. Mod. Phys. 29, 417 (1957).
  31. S. P. Miao, N. C. Tsamis, and R. P. Woodard, J. Math. Phys. (N.Y.) 50, 122502 (2009).
  32. E. O. Kahya, S. P. Miao, and R. P. Woodard, J. Math. Phys. (N.Y.) 53, 022304 (2012).
  33. P. J. Mora, N. C. Tsamis, and R. P. Woodard, J. Math. Phys. (N.Y.) 53, 122502 (2012).
  34. P. J. Mora and R. P. Woodard, Phys. Rev. D 85, 124048 (2012).
  35. K. E. Leonard, T. Prokopec, and R. P. Woodard, arXiv:1211.1342.
  36. B. L. Hu and K. Shiokawa, Phys. Rev. D 57, 3474 (1998).
  37. G. Perez-Nadal, A. Roura, and E. Verdaguer, J. Cosmol. Astropart. Phys. 05 (2010) 036.
  38. N. C. Tsamis and R. P. Woodard, Phys. Rev. D 54, 2621 (1996).

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Phys. Rev. D 87, 044030– Published 15 February, 2013
  • Received 29 October 2012
Article part of CHORUS

© 2013 American Physical Society

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