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Massive relic gravitational waves from f(R) theories of gravity: production and potential detection

The European Physical Journal C volume 65, pages 257–267 (2010)Cite this article

Abstract

The production of a stochastic background of relic gravitational waves is well known in various works in the literature, where, by using the so called adiabatically-amplified zero-point fluctuations process, it has been shown how the standard inflationary scenario for the early universe can in principle provide a distinctive spectrum of relic gravitational waves. In this paper, it is shown that, in general, f(R) theories of gravity produce a third massive polarization of gravitational waves and the primordial production of this polarization is analyzed adapting the adiabatically-amplified zero-point fluctuations process at this case. In this way, previous results, where only particular cases of f(R) theories have been analyzed, will be generalized.

The presence of the mass could also have important applications in cosmology, because the fact that gravitational waves can have mass could give a contribution to the dark matter of the Universe.

An upper bound for these relic gravitational waves, which arises from the WMAP constrains, is also mentioned.

At the end of the paper, the potential detection of such massive gravitational waves using interferometers like Virgo and LIGO is discussed.

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References

  1. F. Acernese et al. (The Virgo Collaboration), Class. Quantum Gravity 24(19), S381–S388 (2007)

    Article  MATH  ADS  Google Scholar 

  2. C. Corda, Astropart. Phys. 27(6), 539–549 (2007) ;

    Article  ADS  Google Scholar 

  3. C. Corda, Int. J. Mod. Phys. D 16(9), 1497–1517 (2007)

    MATH  MathSciNet  ADS  Google Scholar 

  4. B. Willke et al., Class. Quantum Gravity 23(8), S207–S214 (2006)

    Article  ADS  Google Scholar 

  5. D. Sigg (for the LIGO Scientific Collaboration), www.ligo.org/pdf_public/P050036.pdf

  6. B. Abbott et al. (The LIGO Scientific Collaboration), Phys. Rev. D 72, 042002 (2005)

    ADS  Google Scholar 

  7. M. Ando (The TAMA Collaboration), Class. Quantum Gravity 19(7), 1615–1621 (2002)

    Article  Google Scholar 

  8. D. Tatsumi, Y. Tsunesada (The TAMA Collaboration), Class. Quantum Gravity 21(5), S451–S456 (2004)

    Article  ADS  Google Scholar 

  9. C. Corda, J. Cosmol. Astropart. Phys. 4, 009 (2007)

    Google Scholar 

  10. C. Corda, Int. J. Mod. Phys. A 23(10), 1521–1535 (2008)

    Article  MATH  ADS  Google Scholar 

  11. G. Allemandi, M. Francaviglia, M.L. Ruggiero, A. Tartaglia, Gen. Relativ. Gravit. 37, 11 (2005)

    Article  MathSciNet  Google Scholar 

  12. S. Capozziello, C. Corda, Int. J. Mod. Phys. D 15, 1119–1150 (2006)

    MATH  ADS  Google Scholar 

  13. C. Corda, Response of laser interferometers to scalar gravitational waves, in Gravitational Waves Data Analysis Workshop in the General Relativity Trimester of the Institute Henri Poincare, Paris, 13–17 November 2006. On the web in www.luth2.obspm.fr/IHP06/workshops/gwdata/corda.pdf

  14. C. Corda, Astropart. Phys. 28, 247–250 (2007)

    Article  ADS  Google Scholar 

  15. M. Shibata, K. Nakao, T. Nakamura, Phys. Rev. D 50, 7304 (1994)

    ADS  Google Scholar 

  16. M. Maggiore, A. Nicolis, Phys. Rev. D 62, 024004 (2000); also in gr-qc/9907055

    ADS  Google Scholar 

  17. M.E. Tobar, T. Suzuki, K. Kuroda, Phys. Rev. D 59, 102002 (1999)

    ADS  Google Scholar 

  18. K. Nakao, T. Harada, M. Shibata, S. Kawamura, T. Nakamura, Phys. Rev. D 63, 082001 (2001)

    ADS  Google Scholar 

  19. C. Corda, M.F. De Laurentis, in Proceedings of the 10th ICATPP Conference on Astroparticle, Particle, Space Physics, Detectors and Medical Physics—Applications, Villa Olmo, Como, Italy (8–12 October 2007)

  20. C. Corda, Mod. Phys. Lett. A 22(16), 1167–1173 (2007)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  21. S. Capozziello, C. Corda, M.F. De Laurentis, Mod. Phys. Lett. A 22(15), 1097–1104 (2007)

    Article  MATH  ADS  Google Scholar 

  22. C. Corda, Mod. Phys. Lett. A 22(23), 1727–1735 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  23. C. Brans, R.H. Dicke, Phys. Rev. 124, 925 (1961)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  24. N. Bonasia, M. Gasperini, Phys. Rev. D 71, 104020 (2005)

    ADS  Google Scholar 

  25. B. Allen, in Proceedings of the Les Houches School on Astrophysical Sources of Gravitational Waves, ed. by J.-A. Marck, J.-P. Lasota (Cambridge University Press, Cambridge, 1998)

    Google Scholar 

  26. B. Allen, Phys. Rev. D 37, 2078 (1988)

    MathSciNet  ADS  Google Scholar 

  27. L.P. Grishchuk et al., Phys. Uspekhi 44, 1–51 (2001)

    Article  ADS  Google Scholar 

  28. L.P. Grishchuk et al., Uspekhi Fiz. Nauk 171, 3 (2001)

    Article  Google Scholar 

  29. C. Corda, S. Capozziello, M.F. De Laurentis, in Proceedings of the Fourth Italian-Sino Workshop on Relativistic Astrophysics, 20–30 July 2007, Pescara, Italy. AIP Conference Proceedings, vol. 966 (2007), pp. 257–263

  30. S. Capozziello, C. Corda, M.F. De Laurentis, Mod. Phys. Lett. A 22(35), 2647–2655 (2007)

    Article  MATH  ADS  Google Scholar 

  31. C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation (Freeman, New York, 1973)

    Google Scholar 

  32. L. Landau, E. Lifsits, Teoria dei Campi, 3 edn. (Editori Riuniti, Rome, 1999)

    Google Scholar 

  33. E. Elizalde, S. Nojiri, S.D. Odintsov, Phys. Rev. D 70, 043539 (2004)

    ADS  Google Scholar 

  34. G. Cognola, E. Elizalde, S. Nojiri, S.D. Odintsov, L. Sebastiani, S. Zerbini, Phys. Rev. D 77, 046009 (2008)

    ADS  Google Scholar 

  35. T. Inagaky, S. Nojiri, S.D. Odintsov, J. Cosmol. Astropart. Phys. 6, 010 (2005)

    Google Scholar 

  36. G. Watson, An Exposition on Inflationary Cosmology (North Carolina University Press, Chapel Hill, 2000)

    Google Scholar 

  37. A. Guth, Phys. Rev. 23, 347 (1981)

    ADS  Google Scholar 

  38. C.L. Bennett et al., Astrophys. J. Suppl. Ser. 148, 1 (2003)

    Article  ADS  Google Scholar 

  39. D.N. Spergel et al., Astrophys. J. Suppl. Ser. 148, 195 (2003)

    Article  ADS  Google Scholar 

  40. C. Corda, Astropart. Phys. 30(4), 209–215 (2008)

    Article  ADS  Google Scholar 

  41. Private communication with referees

  42. M. Fierz, W. Pauli, Proc. R. Soc. A 173, 211 (1939)

    Article  MathSciNet  ADS  Google Scholar 

  43. M. Fierz, W. Pauli, Helv. Phys. Acta 12, 297 (1939)

    MATH  Google Scholar 

  44. A.A. Logunov, M.A. Mestvirishvili, Theor. Math. Phys. 65, 971 (1986)

    Article  ADS  Google Scholar 

  45. S.S. Gershtein, A.A. Logunov, M.A. Mestvirishvili, Phys. At. Nucl. 61, 1420 (1998)

    Google Scholar 

  46. A.A. Logunov, M.A. Mestvirishvili, gr-qc/9907021

  47. D. Bessada, O. Miranda, Class. Quantum Gravity 26, 045005 (2009); also in 0901.1119 [gr-qc]

    Article  ADS  Google Scholar 

  48. A.A. Starobinsky, Phys. Lett. B 91, 99 (1980)

    ADS  Google Scholar 

  49. A.A. Starobinsky, JETP Lett. 34, 438 (1982)

    ADS  Google Scholar 

  50. S. Capozziello, M.F. De Laurentis, M. Francaviglia, Astropart. Phys. 2(2), 125–129 (2008)

    Article  ADS  Google Scholar 

  51. S. Nojiri, S.D. Odintsov, Int. J. Geom. Methods Mod. Phys. 4, 115–146 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  52. T.P. Sotiriou, V. Faraoni, arXiv:0805.1726

  53. S. Capozziello, M. Francaviglia, Gen. Relativ. Gravit. 40, 2–3 (2008)

    MathSciNet  Google Scholar 

  54. R.A. Hulse, J.H. Taylor, Astrophys. J. Lett. 195, 151 (1975)

    Article  Google Scholar 

  55. S. Capozziello, C. Corda, M.F. De Laurentis, Phys. Lett. B 669(5), 255–259 (2008)

    ADS  Google Scholar 

Download references

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  1. Associazione Galileo Galilei, Via Pier Cironi 16, 59100, Prato, Italy

    Christian Corda

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  1. Christian Corda
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Correspondence to Christian Corda.

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Corda, C. Massive relic gravitational waves from f(R) theories of gravity: production and potential detection. Eur. Phys. J. C 65, 257–267 (2010). https://doi.org/10.1140/epjc/s10052-009-1100-5

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  • DOI: https://doi.org/10.1140/epjc/s10052-009-1100-5

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