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International Journal of Theoretical Physics

, Volume 52, Issue 8, pp 2722–2734 | Cite as

Quintom Potentials from Quantum Cosmology Using the FRW Cosmological Model

  • J. Socorro
  • Priscila Romero
  • Luis O. Pimentel
  • M. Aguero
Article

Abstract

We construct the quintom potential of dark energy models in the framework of spatially flat Friedmann–Robertson Walker universe in the inflationary epoch, using the Bohm like approach, known as amplitude-real-phase. We find some potentials for which the wave function of the universe is found analytically and we have obtained the classical trajectories in the inflation era.

Keywords

Quantum cosmology Quintom potentials Classical and quantum solutions 

Notes

Acknowledgements

This work was partially supported by CONACYT 179881 grant. DAIP (2011–2012) and PROMEP grants UGTO-CA-3, UAM-I-43. PRB and MA were partially supported by UAEMex grant FEO1/2012 103.5/12/2126. This work is part of the collaboration within the Instituto Avanzado de Cosmología, and Red PROMEP: Gravitation and Mathematical Physics under project Quantum aspects of gravity in cosmological models, phenomenology and geometry of space-time. Many calculations were done by Symbolic Program REDUCE 3.8.

References

  1. 1.
    Copeland, E.J., Sami, M., Tsujikawa, S.: Int. J. Mod. Phys. D 15, 1753 (2006). arXiv:hep-th/0603057 ADSMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
  3. 3.
    Cai, Y.F., Saridakis, E.N., Setare, M.R., Xia, J.Q.: Phys. Rep. 493, 1 (2010) ADSCrossRefMathSciNetGoogle Scholar
  4. 4.
    Guo, Z.K., Piao, Y.S., Zhang, X., Zhang, Y.Z.: Phys. Lett. B 608, 177 (2005) ADSCrossRefGoogle Scholar
  5. 5.
    Feng, B., Wang, X., Zhang, X.: Phys. Lett. B 607, 35 (2005) ADSCrossRefGoogle Scholar
  6. 6.
    Sadjadi, H.M., Alimohammadi, M.: Phys. Rev. D 74(4), 043506 (2006) ADSCrossRefGoogle Scholar
  7. 7.
    Guo, Z.K., Piao, Y.S., Zhang, X., Zhang, Y.Z.: Phys. Rev. D 74(12), 127304 (2006) ADSCrossRefGoogle Scholar
  8. 8.
    Feng, B., Li, M., Piao, Y.S., Zhang, X.: Phys. Lett. B 634, 101 (2006) ADSCrossRefGoogle Scholar
  9. 9.
    Zhao, W., Zhang, Y.: Phys. Rev. D 73(12), 123509 (2006) ADSCrossRefGoogle Scholar
  10. 10.
    Cai, Y.F., Li, M., Lu, J.X., Piao, Y.S., Qiu, T., Zhang, X.: Phys. Lett. B 651, 1 (2007) ADSMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Cai, Y.F., Qiu, T., Zhang, X., Piao, Y.S., Li, M.: J. High Energy Phys. 10, 71 (2007) ADSCrossRefGoogle Scholar
  12. 12.
    Alimohammadi, M., Sadjadi, H.M.: Phys. Lett. B 648, 113 (2007) ADSCrossRefGoogle Scholar
  13. 13.
    Lazkoz, R., León, G., Quiros, I.: Phys. Lett. B 649, 103 (2007) ADSMATHCrossRefGoogle Scholar
  14. 14.
    Cai, Y.F., Qiu, T., Brandenberger, R., Piao, Y.S., Zhang, X.: J. Cosmol. Astropart. Phys. 3, 13 (2008) ADSCrossRefGoogle Scholar
  15. 15.
    Cai, Y.F., Wang, J.: Class. Quantum Gravity 25(16), 165014 (2008) ADSCrossRefMathSciNetGoogle Scholar
  16. 16.
    Zhang, S., Chen, B.: Phys. Lett. B 669, 4 (2008) ADSCrossRefMathSciNetGoogle Scholar
  17. 17.
    Sadeghi, J., Setare, M.R., Banijamali, A., Milani, F.: Phys. Lett. B 662, 92 (2008) ADSCrossRefGoogle Scholar
  18. 18.
    Nozari, K., Setare, M.R., Azizi, T., Behrouz, N.: Phys. Scr. 80(2), 025901 (2009) ADSCrossRefGoogle Scholar
  19. 19.
    Setare, M.R., Saridakis, E.N.: Phys. Rev. D 79(4), 043005 (2009) ADSCrossRefMathSciNetGoogle Scholar
  20. 20.
    Setare, M.R., Saridakis, E.N.: Int. J. Mod. Phys. D 18(4), 549 (2009) ADSMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Sadeghi, J., Setare, M.R., Banijamali, A.: Phys. Lett. B 678, 164 (2009) ADSCrossRefMathSciNetGoogle Scholar
  22. 22.
    Qiu, T.: Mod. Phys. Lett. A 25, 909 (2010) ADSMATHCrossRefGoogle Scholar
  23. 23.
    Saridakis, E.N.: Nucl. Phys. B 830, 374 (2010) ADSMATHCrossRefGoogle Scholar
  24. 24.
    Amani, A.R.: Int. J. Theor. Phys. 50, 3078 (2011) MATHCrossRefGoogle Scholar
  25. 25.
    Farajollahi, H., Shahabi, A., Salehi, A.: Astron. Astrophys. Suppl. Ser. 338, 205 (2012) MATHGoogle Scholar
  26. 26.
    Guo, S.-K., Piao, Y.-S., Zhang, X., Zhang, Y.-Z.: Phys. Lett. B 608, 177 (2005). arXiv:astro-ph/0410654 ADSCrossRefGoogle Scholar
  27. 27.
    Chimento, L.P., Forte, M., Lazkoz, R., Richarte, M.G.: Phys. Rev. D 79(4), 043502 (2009) ADSCrossRefGoogle Scholar
  28. 28.
    Adak, D., Bandyopadhyay, A., Majumdar, D.: (2011) arXiv:1103.1533
  29. 29.
    Guzmán, W., Sabido, M., Socorro, J., Ureña-López, A.L.: Int. J. Mod. Phys. D 16(4), 641–653 (2007) ADSMATHCrossRefGoogle Scholar
  30. 30.
    Socorro, J., D’oleire, M.: Phys. Rev. D 82(4), 044008 (2010) ADSCrossRefGoogle Scholar
  31. 31.
    Bohm, D.: Phys. Rev. 85(2), 166 (1952) ADSMATHCrossRefMathSciNetGoogle Scholar
  32. 32.
    Moncrief, V., Ryan, M.P.: Phys. Rev. D 44, 2375 (1991) ADSCrossRefMathSciNetGoogle Scholar
  33. 33.
    Kodama, H.: Prog. Theor. Phys. 80, 1024 (1988) ADSCrossRefMathSciNetGoogle Scholar
  34. 34.
    Kodama, H.: Phys. Rev. D 42, 2548 (1990) ADSCrossRefMathSciNetGoogle Scholar
  35. 35.
    Melchiorri, A., Mersini, L., Odmann, C.J., Trodden, M.: arXiv:astro-ph/0211522
  36. 36.
    Sáez, D., Ballester, V.J.: Phys. Lett. A 113, 467 (1986) ADSCrossRefGoogle Scholar
  37. 37.
    Socorro, J., Sabido, M., Sánchez G., M.A., Frías Palos, M.G.: Rev. Mex. Fis. 56(2), 166–171 (2010). arXiv:1007.3306 Google Scholar
  38. 38.
    Sabido, M., Socorro, J., Ureña-López, A.L.: Fizika B 19(4), 177–186 (2010). arXiv:0904.0422 Google Scholar
  39. 39.
    Socorro, J., Rodríguez Espinoza-García A, P.A., Pimentel, L.O., Romero, P.: Cosmological Bianchi class a models in Sáez–Ballester theory. In: Alfonso-Faus, A. (ed.) Aspects of Today’s Cosmology, InTech, pp. 185–204 (2011) Google Scholar
  40. 40.
    Hartle, J., Hawking, S.W.: Phys. Rev. D 28, 2960 (1983) ADSCrossRefMathSciNetGoogle Scholar
  41. 41.
    Barbosa, G.D., Pinto-Neto, N.: Phys. Rev. D 70, 103512 (2004) ADSCrossRefMathSciNetGoogle Scholar
  42. 42.
    León, G., Leyva, Y., Socorro, J.: arXiv:1208.0061 [gr-qc]
  43. 43.
    Perlmutter, S., et al.: Astrophys. J. 517, 565 (1999) ADSCrossRefGoogle Scholar
  44. 44.
    Cline, J.M., Jeon, S., Moore, G.D.: Phys. Rev. D 70, 043543 (2004) ADSCrossRefGoogle Scholar
  45. 45.
    Nojiri, S., Odintsov, S.D.: Phys. Lett. B 571, 1 (2003) ADSMATHCrossRefGoogle Scholar
  46. 46.
    Nojiri, S., Odintsov, S.D.: Phys. Lett. B 562, 147 (2003) ADSMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • J. Socorro
    • 1
    • 2
  • Priscila Romero
    • 3
  • Luis O. Pimentel
    • 2
  • M. Aguero
    • 3
  1. 1.Departamento de Física, DCeIUniversidad de Guanajuato-Campus LeónLeónMexico
  2. 2.Departamento de FísicaUniversidad Autónoma MetropolitanaMéxicoMexico
  3. 3.Facultad de Ciencias de la Universidad Autónoma del Estado de MéxicoTolucaMexico

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