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Cosmic Acceleration and f (R) Theory: Perturbed Solution in a Matter FLRW Model

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Abstract

In the present paper we consider f (R) gravity theories in the metric approach and we derive the equations of motion, focusing also on the boundary conditions. In such a way we apply the general equations to a first order perturbation expansion of the Lagrangian. We present a model able to fit supernovae data without introducing dark energy.

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References

  1. Weyl Ann, H.: Physics 59, 101 (1919)

    Google Scholar 

  2. Eddington, A.S.: The Mathematical Theory of Relativity. Cambridge University Press (1923)

  3. Buchdahl, H.A.: Mon. Not. R. Astron. Soc 150, 1 (1970)

    Article  ADS  Google Scholar 

  4. Utiyama, R., De Witt, B.S.: J. Math. Phys. 3, 608 (1962)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  5. Amendola, L., Gannouji, R., Polarski, D., Tsujikawa, S.: Phys. Rev. D 75, 083504 (2007)

    Article  ADS  Google Scholar 

  6. Silvestri, A., Trodden, M.: Rept. Prog. Phys. 72, 096901 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  7. Sotiriou, T.P., Faraoni, V.: Rev. Mod. Phys 82, 451 (2010)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  8. Capozziello, S., Faraoni, V.: Beyond Einstein Gravity. Springer, New York (2010)

    Google Scholar 

  9. De Felice, A., Tsujikawa, S.: Living Rev. Relativ. 13, 3 (2010)

    Article  ADS  Google Scholar 

  10. Capozziello, S., De Laurentis, M.: Phys. Rep 509, 167 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  11. Sotoriou, T.P, Faraoni, V.: Rev. Mod. Phys 82, 451 (2010)

    Article  ADS  Google Scholar 

  12. Felice, A.D., Tsujikawa, T.: Living Rev. Rel. 13, 39 (2010)

    Google Scholar 

  13. Nojiri, S., Odintsov, S.D.: Phys. Rep. 1011.0544

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

    Article  ADS  Google Scholar 

  15. Capozziello, S., Francaviglia, M.: Gen. Rel. Grav 40, 357 (2008)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  16. Chiba, T.: Phys. Lett B 575, 1 (2003)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  17. Biswas, T., Gerwick, E., Koivisto, T., Mazumdar, A.: Phys. Rev. Lett. 108, 031101 (2012)

    Article  ADS  Google Scholar 

  18. Biswas, T., Conroy, A., Koshelev, A. S., Mazumdar, A: Class. Quant. Grav. 31, 015022 (2014). [Erratum-ibid. 31 (2014) 159501]

    Article  ADS  MathSciNet  Google Scholar 

  19. Riess, A.G., et al.: Astron. J 116, 1009 (1998)

    Article  ADS  Google Scholar 

  20. Perlmutter, S., et al.: Astrophys. J 517, 565 (1999)

    Article  ADS  Google Scholar 

  21. Tonry, J.L., et al.: Astrophys. J 594, 1 (2003)

    Article  ADS  Google Scholar 

  22. Carrol, S.M., Duvvuri, V., Trodden, M., Turner, M.S.: Phys. Rev D 70, 043528 (2004)

    Article  ADS  Google Scholar 

  23. Nojiri, S., Odintsov, S.D.: Int. J. Geom. Methods Mod. Phys 4, 115 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  24. Capozziello, S.: Int. J. Mod. Phys. D 11, 483 (2002)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  25. Capozziello, S., Carloni, S., Troisi, A.: Recent Res. Dev. Astron. Astrophys 1, 625 (2003)

    Google Scholar 

  26. Nojiri, S., Odintsov, S.D.: Phys. Rev. D 68, 123512 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  27. Nojiri, S., Odintsov, S.D.: Phys. Lett. B 576, 5 (2003)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  28. Faraoni, V.: Phys. Rev. D 72, 124005 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  29. de la Cruz-Dombriz, A, Dobado, A.: Phys. Rev. D 74, 087501 (2006)

    Article  ADS  Google Scholar 

  30. Poplawski, N.J.: Phys. Rev. D 74, 084032 (2006)

    Article  ADS  Google Scholar 

  31. Brookfield, A.W., van de Bruck, C., Hall, L.M.H.: Phys. Rev. D 74, 064028 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  32. Li, B., Chan, K.-C., Chu, M.-C.: Phys. Rev. D 76, 024002 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  33. Sotiriou, T.P., Liberati, S.: Ann. Phys 322, 935 (2007)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  34. Sotiriou, T.P.: Phys. Lett. B 645, 389 (2007)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  35. Sotiriou, T.P.: Class. Quant. Grav 23, 5117 (2006)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  36. Bean, R., Bernat, D., Pogosian, L., Silvestri, A., Trodden, M.: Phys. Rev. D 75, 064020 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  37. Baghram, S., Farhang, M., Rahvar, S.: Phys. Rev. D 75, 044024 (2007)

    Article  ADS  Google Scholar 

  38. Bazeia, D., Carneiro da Cunha, B., Menezes, R., Petrov, A.Y.: Phys. Lett. B 649, 445 (2007)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  39. Li, B., Barrow, J.D.: Phys. Rev. D 75, 084010 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  40. Rador, T.: Phys. Rev. D 75, 064033 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  41. Sokolowski, L.M.: Class. Quant. Grav 24, 3391 (2007)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  42. Faraoni, V.: Phys. Rev. D 74, 104017 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  43. Faraoni, V.: Phys. Rev. D 75, 067302 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  44. Nojiri, S., Odintsov, S.D.: Gen. Rel. Grav 36, 1765 (2004)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  45. Meng, X.-H., Wang, P.: Gen. Rel. Grav 36, 1947 (2004)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  46. Abdalla, M.C.B., Nojiri, S.’i., Odintsov, S.D.: Class. Quant. Grav 22, L35 (2005)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  47. Capozziello, S., Cardone, V.F., Troisi, A.: Phys. Rev. D 71, 043503 (2005)

    Article  ADS  Google Scholar 

  48. Allemandi, G., Borowiec, A., Francaviglia, M., Odintsov, S.D.: Phys. Rev. D 72, 063505 (2005)

    Article  ADS  Google Scholar 

  49. Koivisto, T., Kurki-Suonio, H.: Class. Quant. Grav 23, 2355 (2006)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  50. Hu, W., Sawicki, I.: Phys. Rev. D 76, 064004 (2007)

    Article  ADS  Google Scholar 

  51. Mena, O., Santiago, J., Weller, J.: Phys. Rev. Lett. 96, 041103 (2006)

    Article  ADS  Google Scholar 

  52. Brevik, I.H.: Int. J. Mod. Phys. D 15, 767 (2006)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  53. Capozziello, S., Garattini, R.: Class. Quant. Grav 24, 1627 (2007)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  54. Nojiri, S., Odintsov, S.D.: Phys. Rev. D 74, 086005 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  55. Nojiri, S., Odintsov, S.D.: J. Phys. A 40, 6725 (2007)

    Article  ADS  MATH  Google Scholar 

  56. Capozziello, S., Nojiri, S., Odintsov, S.D., Troisi, A.: Phys. Lett. B 639, 135 (2006)

    Article  ADS  Google Scholar 

  57. Fay, S., Nesseris, S., Perivolaropoulos, L.: Phys. Rev. D 76, 063504 (2007)

    Article  ADS  Google Scholar 

  58. Fay, S., Tavakol, R., Tsujikawa, S.: Phys. Rev. D 75, 063509 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  59. Nojiri, S., Odintsov, S.D., Sasaki, M.: Phys. Rev. D 71, 123509 (2005)

    Article  ADS  Google Scholar 

  60. Sami, M., Toporensky, A., Tretjakov, P.V., Tsujikawa, S.: Phys. Lett. B 619, 193 (2005)

    Article  ADS  Google Scholar 

  61. Song, Y.S., Hu, W., Sawicki, I.: Phys. Rev. D 75, 044004 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  62. Capozziello, S., Lambiase, G.: arXiv:1304.5640

  63. Dyer, E., Hinterbichler, K.: Phys. Rev. D 79, 024028 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  64. Guarnizo, A., Castaneda, L., Tejeiro, J.M.: Gen. Rel. Grav 42, 2713 (2010)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  65. Amanulah, A., et al.: The supernova cosmology projiect. Astrophys. J 716, 712 (2010)

    Article  ADS  Google Scholar 

  66. Cosmai, L., Fanizza, G., Gasperini, M., Tedesco, L.: Class. Quant. Grav. 30, 095011 (2013)

    Article  ADS  Google Scholar 

  67. Fanizza, G., Tedesco, L.: Phys. Rev. D 91, 023006 (2015)

    Article  ADS  Google Scholar 

  68. Capozziello, S., Carloni, S., Troisi, A.: Astron. Astrophys. 1, 625 (2003)

    Google Scholar 

  69. Capozziello, S., Cardone, V.F., Carloni, S., Troisi, A.: Intern. J. Mod Phys. D 12, 1969 (2003)

    Article  ADS  Google Scholar 

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Acknowledgments

The authors would like to thank M. Gasperini for useful discussions. This work is supported by the research grant “Theoretical Astroparticle Physics” No. 2012CPPYP7 under the program PRIN 2012 funded by the Ministero dell’Istruzione, Università e della Ricerca (MIUR). This work is also supported by the italian Istituto Nazionale di Fisica Nucleare (INFN) through the “Theoretical Astroparticle Physics” (TASP) project.

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Authors and Affiliations

  1. Istituto Nazionale di Fisica Nucleare, Sezione di Bari, Bari, Italy

    L. Cosmai, G. Fanizza & L. Tedesco

  2. Dipartimento di Fisica, Università di Bari, Via G. Amendola 173, 70126, Bari, Italy

    G. Fanizza & L. Tedesco

  3. Departement de Physique Theorique, Universite de Geneve, 24 quai Ernest-Ansermet, CH-1211, Geneve 4, Switzerland

    G. Fanizza

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  1. L. Cosmai
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  2. G. Fanizza
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  3. L. Tedesco
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Correspondence to L. Tedesco.

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Cosmai, L., Fanizza, G. & Tedesco, L. Cosmic Acceleration and f (R) Theory: Perturbed Solution in a Matter FLRW Model. Int J Theor Phys 55, 754–765 (2016). https://doi.org/10.1007/s10773-015-2713-0

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  • DOI: https://doi.org/10.1007/s10773-015-2713-0

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