Skip to main content
SpringerLink
Log in

A multi-field tachyon-quintom model of dark energy and fate of the universe

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

We investigate a multi-field model of dark energy in this paper. We develop a model of dark energy with two multiple scalar fields: one we consider is a multi-field tachyon and the other is multi-field phantom tachyon scalars. We make an analysis of the system in phase space by considering inverse square potentials suitable for these models. Through the development of an autonomous dynamical system, the critical points and their stability analysis is performed. It has been observed that these stable critical points are satisfied by power-law solutions. Moving on toward the analysis, we can predict the fate of the universe. A special feature of this model is that it affects the equation of state parameter w to alter from being it greater than \(-\,1\) to be less than it during the evolutionary phase of the universe. Thus, it’s all about the phantom divide which turns out to be decisive in the evolution of the cosmos in these models.

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

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. A.G. Riess, A.V. Filippenko, P. Challis, A. Clocchiatti, A. Diercks, P.M. Garnavich, J. Tonry, Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116(3), 1009 (1998)

    Article  ADS  Google Scholar 

  2. S. Perlmutter, G. Aldering, G. Goldhaber, R.A. Knop, P. Nugent, P.G. Castro, Supernova cosmology project. Measurements of and from 42 high-redshift supernovae. Astrophys. J. 517(2), 565 (1999)

    Article  ADS  MATH  Google Scholar 

  3. A.G. Riess, P.E. Nugent, R.L. Gilliland, B.P. Schmidt, J. Tonry, M. Dickinson, S. Veilleux, The farthest known supernova: support for an accelerating universe and a glimpse of the epoch of deceleration. Astrophys. J. 560(1), 49 (2001)

    Article  ADS  Google Scholar 

  4. J.L. Tonry, B.P. Schmidt, B. Barris, P. Candia, P. Challis, A. Clocchiatti, N.B. Suntzeff, Cosmological results from high-z supernovae. Astrophys. J. 594(1), 1 (2003)

    Article  ADS  Google Scholar 

  5. P. Astier, R. Pain, Observational evidence of the accelerated expansion of the universe. C. R. Phys. 13(6–7), 521–538 (2012)

    Article  ADS  Google Scholar 

  6. Y. Yang, Y. Gong, The evidence of cosmic acceleration and observational constraints. J. Cosmol. Astropart. Phys. 2020(06), 059 (2020)

    Article  MathSciNet  Google Scholar 

  7. A.G. Riess, The expansion of the Universe is faster than expected. Nat. Rev. Phys. 2(1), 10–12 (2020)

    Article  MathSciNet  Google Scholar 

  8. D. Rubin, J. Heitlauf, Is the expansion of the universe accelerating? All signs still point to yes: a local dipole anisotropy cannot explain dark energy. Astrophys. J. 894(1), 68 (2020)

    Article  ADS  Google Scholar 

  9. M. Tegmark, M.A. Strauss, M.R. Blanton, K. Abazajian, S. Dodelson, H. Sandvik, D.G. York, Cosmological parameters from SDSS and WMAP. Phys. Rev. D 69(10), 103501 (2004)

    Article  ADS  MATH  Google Scholar 

  10. B.D. Sherwin, J. Dunkley, S. Das, J.W. Appel, J.R. Bond, C.S. Carvalho, E. Wollack, Evidence for dark energy from the cosmic microwave background alone using the Atacama Cosmology Telescope lensing measurements. Phys. Rev. Lett. 107(2), 021302 (2011)

    Article  ADS  Google Scholar 

  11. Z.L. Tu, J. Hu, F.Y. Wang, Probing cosmic acceleration by strong gravitational lensing systems. Mon. Not. R. Astron. Soc. 484(3), 4337–4346 (2019)

    ADS  Google Scholar 

  12. N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, G. Roudier, Planck 2018 results-VI. Cosmological parameters. Astron. Astrophys. 641, A6 (2020)

    Article  Google Scholar 

  13. J. Yoo, Y. Watanabe, Theoretical models of dark energy. Int. J. Mod. Phys. D 21(12), 1230002 (2012)

    Article  ADS  MATH  Google Scholar 

  14. H. Wei, S.N. Zhang, How to distinguish dark energy and modified gravity? Phys. Rev. D 78(2), 023011 (2008)

    Article  ADS  Google Scholar 

  15. V. Faraoni, S. Capozziello, Beyond Einstein Gravity: A Survey of Gravitational Theories for Cosmology and Astrophysics (Springer, Berlin, 2011)

    Book  MATH  Google Scholar 

  16. C.J. Feng, X.H. Zhai, X.Z. Li, Multi-pole dark energy. Chin. Phys. C 44(10), 105103 (2020)

    Article  ADS  Google Scholar 

  17. E.J. Copeland, M. Sami, S. Tsujikawa, Dynamics of dark energy. Int. J. Mod. Phys. D 15(11), 1753–1935 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. A. Einstein, Cosmological Considerations in the General Theory of Relativity, Math. Phys., 1917, 142–152 (1917)

  19. C. Armendariz-Picon, V. Mukhanov, P.J. Steinhardt, Dynamical solution to the problem of a small cosmological constant and late-time cosmic acceleration. Phys. Rev. Lett. 85(21), 4438 (2000)

    Article  ADS  Google Scholar 

  20. P.J.E. Peebles, B. Ratra, The cosmological constant and dark energy. Rev. Mod. Phys. 75(2), 559 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. G.Z. Kang, D.S. Zhang, L. Jun, H.S. Zong, Fine tuning problem of the cosmological constant in a generalized Randall–Sundrum model. Chin. Phys. C 44(12), 125102 (2020)

    Article  ADS  Google Scholar 

  22. J.J. Zhang, C.C. Lee, C.Q. Geng, Observational constraints on running vacuum model. Chin. Phys. C 43(2), 025102 (2019)

    Article  ADS  Google Scholar 

  23. P.J.E. Peebles, B. Ratra, Cosmology with a time-variable cosmological ‘constant’. Astrophys. J. 325, L17–L20 (1988)

    Article  ADS  Google Scholar 

  24. E.J. Copeland, M. Sami, S. Tsujikawa, Dynamics of dark energy, hep-th/0603057

  25. M. Sami, Models of dark energy, in The Invisible Universe: Dark Matter and Dark Energy, (Springer, Berlin, Heidelberg, 2007), pp. 219–256

  26. C.A.I. Rong-Gen, On theoretical models of dark energy. Chin. Phys. C 31(9), 827–834 (2007)

    Google Scholar 

  27. S. Bahamonde, C.G. Böhmer, S. Carloni, E.J. Copeland, W. Fang, N. Tamanini, Dynamical systems applied to cosmology dark energy and modified gravity. Phys. Rep. 775, 1–122 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  28. M. Li, X.D. Li, S. Wang, Y. Wang, Dark energy: a brief review. Front. Phys. 8(6), 828–846 (2013)

    Article  ADS  Google Scholar 

  29. B. Ratra, P.J. Peebles, Cosmological consequences of a rolling homogeneous scalar field. Phys. Rev. D 37(12), 3406 (1988)

    Article  ADS  Google Scholar 

  30. P.J. Steinhardt, A quintessential introduction to dark energy. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 361(1812), 2497–2513 (2003)

    Article  ADS  MATH  Google Scholar 

  31. Z.K. Guo, N. Ohta, Y.Z. Zhang, Parametrization of quintessence and its potential. Phys. Rev. D 72(2), 023504 (2005)

    Article  ADS  Google Scholar 

  32. Z.K. Guo, N. Ohta, Y.Z. Zhang, Parametrizations of the dark energy density and scalar potentials. Mod. Phys. Lett. A 22(12), 883–890 (2007)

    Article  ADS  MATH  Google Scholar 

  33. J.Z. Qi, M.J. Zhang, W.B. Liu, Dynamical evolution of quintessence cosmology in a physical phase space. Int. J. Theor. Phys. 55(8), 3672–3681 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  34. Hughes, J. The quintessential dark energy theory: quintessence (2019)

  35. I. Zlatev, L. Wang, P.J. Steinhardt, Quintessence, cosmic coincidence, and the cosmological constant. Phys. Rev. Lett. 82(5), 896 (1999)

    Article  ADS  Google Scholar 

  36. T. Barreiro, E.J. Copeland, N.A. Nunes, Quintessence arising from exponential potentials. Phys. Rev. D 61(12), 127301 (2000)

    Article  ADS  Google Scholar 

  37. T. Chiba, T. Okabe, M. Yamaguchi, Kinetically driven quintessence. Phys. Rev. D 62(2), 023511 (2000)

    Article  ADS  Google Scholar 

  38. C. Armendariz-Picon, T. Damour, V.I. Mukhanov, k-inflation. Phys. Lett. B 458(2–3), 209–218 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  39. C. Armendariz-Picon, V. Mukhanov, P.J. Steinhardt, Essentials of k-essence. Phys. Rev. D 63(10), 103510 (2001)

    Article  ADS  Google Scholar 

  40. Y. Rong-Jia, G. Xiang-Ting, Observational constraints on purely kinetic k-essence dark energy models. Chin. Phys. Lett. 26(8), 089501 (2009)

    Article  ADS  Google Scholar 

  41. S. Sur, S. Das, Multiple kinetic k-essence, phantom barrier crossing and stability. J. Cosmol. Astropart. Phys. 2009(01), 007 (2009)

    Article  Google Scholar 

  42. R.J. Scherrer, Purely kinetic k-essence as unified dark matter. Phys. Rev. Lett. 93(1), 011301 (2004)

    Article  ADS  Google Scholar 

  43. M. Sami, A. Toporensky, Phantom field and the fate of the universe. Mod. Phys. Lett. A 19(20), 1509–1517 (2004)

    Article  ADS  Google Scholar 

  44. J.M. Cline, S. Jeon, G.D. Moore, The phantom menaced: constraints on low-energy effective ghosts. Phys. Rev. D 70(4), 043543 (2004)

    Article  ADS  Google Scholar 

  45. M. Sami, A. Toporensky, P.V. Tretjakov, S. Tsujikawa, The fate of (phantom) dark energy universe with string curvature corrections. Phys. Lett. B 619(3–4), 193–200 (2005)

    Article  ADS  Google Scholar 

  46. A. Vikman, Can dark energy evolve to the phantom? Phys. Rev. D 71(2), 023515 (2005)

    Article  ADS  Google Scholar 

  47. J. Kujat, R.J. Scherrer, A.A. Sen, Phantom dark energy models with negative kinetic term. Phys. Rev. D 74(8), 083501 (2006)

    Article  ADS  Google Scholar 

  48. W. Wen-Fu, S. Zheng-Wei, T. Bin, Exact solution of phantom dark energy model. Chin. Phys. B 19(11), 119801 (2010)

    Article  ADS  Google Scholar 

  49. R.R. Caldwell, M. Kamionkowski, N.N. Weinberg, Phantom energy: dark energy with w1 causes a cosmic doomsday. Phys. Rev. Lett. 91(7), 071301 (2003)

    Article  ADS  Google Scholar 

  50. W. Hu, Crossing the phantom divide: dark energy internal degrees of freedom. Phys. Rev. D 71(4), 071301 (2005)

    Article  Google Scholar 

  51. S.M. Carroll, M. Hoffman, M. Trodden, Can the dark energy equation-of-state parameter w be less than 1? Phys. Rev. D 68(2), 023509 (2003)

    Article  ADS  Google Scholar 

  52. Z.K. Guo, Y.Z. Zhang, Interacting phantom energy. Phys. Rev. D 71(2), 023501 (2005)

    Article  ADS  Google Scholar 

  53. K.J. Ludwick, The viability of phantom dark energy: a review. Mod. Phys. Lett. A 32(28), 1730025 (2017)

    Article  ADS  Google Scholar 

  54. R.R. Caldwell, M. Kamionkowski, N.N. Weinberg, Phantom energy and cosmic doomsday (2003). arXiv preprint arXiv:astro-ph/0302506

  55. W. Fang, H. Tu, J. Huang, C. Shu, Dynamical system of scalar field from 2-dimension to 3-D and its cosmological implications. Eur. Phys. J. C 76(9), 1–12 (2016)

    Article  Google Scholar 

  56. R.J. Scherrer, Phantom dark energy, cosmic doomsday, and the coincidence problem. Phys. Rev. D 71(6), 063519 (2005)

    Article  ADS  Google Scholar 

  57. H. Štefančić, Dark energy transition between quintessence and phantom regimes: an equation of state analysis. Phys. Rev. D 71(12), 124036 (2005)

    Article  ADS  Google Scholar 

  58. B. Feng, X. Wang, X. Zhang, Dark energy constraints from the cosmic age and supernova. Phys. Lett. B 607(1–2), 35–41 (2005)

    Article  ADS  Google Scholar 

  59. Z.K. Guo, Y.S. Piao, X. Zhang, Y.Z. Zhang, Cosmological evolution of a quintom model of dark energy. Phys. Lett. B 608(3–4), 177–182 (2005)

    Article  ADS  Google Scholar 

  60. X.F. Zhang, H. Li, Y.S. Piao, X. Zhang, Two-field models of dark energy with equation of state across-1. Mod. Phys. Lett. A 21(03), 231–241 (2006)

    Article  ADS  Google Scholar 

  61. Y.F. Cai, M. Li, J.X. Lu, Y.S. Piao, T. Qiu, X. Zhang, A string-inspired quintom model of dark energy. Phys. Lett. B 651(1), 1–7 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  62. B. Feng, M. Li, Y.S. Piao, X. Zhang, Oscillating quintom and the recurrent universe. Phys. Lett. B 634(2–3), 101–105 (2006)

    Article  ADS  Google Scholar 

  63. Z.K. Guo, Y.S. Piao, X. Zhang, Y.Z. Zhang, Two-field quintom models in the w w plane. Phys. Rev. D 74(12), 127304 (2006)

    Article  ADS  Google Scholar 

  64. Y.F. Cai, H. Li, Y.S. Piao, X. Zhang, Cosmic duality in quintom universe. Phys. Lett. B 646(4), 141–144 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  65. Y.F. Cai, T. Qiu, X. Zhang, Y.S. Piao, M. Li, Bouncing universe with quintom matter. J. High Energy Phys. 2007(10), 071 (2007)

    Article  Google Scholar 

  66. S. Mishra, S. Chakraborty, Dynamical system analysis of quintom dark energy model. Eur. Phys. J. C 78(11), 1–9 (2018)

    Article  Google Scholar 

  67. S. Panpanich, P. Burikham, S. Ponglertsakul, L. Tannukij, Resolving Hubble tension with quintom dark energy model. Chin. Phys. C 45(1), 015108 (2021)

    Article  ADS  Google Scholar 

  68. A. Mazumdar, S. Panda, A. Perez-Lorenzana, Assisted inflation via tachyon condensation. Nucl. Phys. B 614(1–2), 101–116 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  69. Y.S. Piao, R.G. Cai, X. Zhang, Y.Z. Zhang, Assisted tachyonic inflation. Phys. Rev. D 66(12), 121301 (2002)

    Article  ADS  Google Scholar 

  70. Z.K. Guo, Y.S. Piao, R.G. Cai, Y.Z. Zhang, Inflationary attractor from tachyonic matter. Phys. Rev. D 68(4), 043508 (2003)

    Article  ADS  Google Scholar 

  71. L. Kofman, A. Linde, Problems with tachyon inflation. J. High Energy Phys. 2002(07), 004 (2002)

    Article  MathSciNet  Google Scholar 

  72. S. Ashoke. Remarks on tachyon driven cosmology, String Theory Cosmol., pp. 70–75 (2005)

  73. T. Padmanabhan, Accelerated expansion of the universe driven by tachyonic matter. Phys. Rev. D 66(2), 021301 (2002)

    Article  ADS  Google Scholar 

  74. E.J. Copeland, A.R. Liddle, D. Wands, Exponential potentials and cosmological scaling solutions. Phys. Rev. D 57(8), 4686 (1998)

    Article  ADS  Google Scholar 

  75. G.W. Gibbons, Cosmological evolution of the rolling tachyon. Phys. Lett. B 537(1–2), 1–4 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  76. J.G. Hao, X.Z. Li, Reconstructing the equation of state of the tachyon. Phys. Rev. D 66(8), 087301 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  77. G.W. Gibbons, Thoughts on tachyon cosmology. Class. Quantum Gravity 20(12), S321 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  78. L.R. Abramo, F. Finelli, Cosmological dynamics of the tachyon with an inverse power-law potential. Phys. Lett. B 575(3–4), 165–171 (2003)

    Article  ADS  MATH  Google Scholar 

  79. J.S. Bagla, H.K. Jassal, T. Padmanabhan, Cosmology with tachyon field as dark energy. Phys. Rev. D 67(6), 063504 (2003)

    Article  ADS  Google Scholar 

  80. Z.K. Guo, Y.S. Piao, Y.Z. Zhang, Cosmological scaling solutions and multiple exponential potentials. Phys. Lett. B 568(1–2), 1–7 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  81. V. Gorini, A. Kamenshchik, U. Moschella, V. Pasquier, Tachyons, scalar fields, and cosmology. Phys. Rev. D 69(12), 123512 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  82. M. Sami, P. Chingangbam, T. Qureshi, Cosmology with rolling tachyon. Pramana 62(3), 765–770 (2004)

    Article  ADS  Google Scholar 

  83. G. Calcagni, A.R. Liddle, Tachyon dark energy models: dynamics and constraints. Phys. Rev. D 74(4), 043528 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  84. E.J. Copeland, M.R. Garousi, M. Sami, S. Tsujikawa, What is needed of a tachyon if it is to be the dark energy? Phys. Rev. D 71(4), 043003 (2005)

    Article  ADS  Google Scholar 

  85. Y. Shao, Y.X. Gui, W. Wang, Parametrization of tachyon field. Mod. Phys. Lett. A 22(16), 1175–1181 (2007)

    Article  ADS  MATH  Google Scholar 

  86. Y. Shao, Y. Gui, Statefinder parameters for tachyon dark energy model. Mod. Phys. Lett. A 23(01), 65–71 (2008)

    Article  ADS  MATH  Google Scholar 

  87. C.J.A.P. Martins, F.M.O. Moucherek, Cosmological and astrophysical constraints on tachyon dark energy models. Phys. Rev. D 93(12), 123524 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  88. A. Singh, A. Sangwan, H.K. Jassal, Low redshift observational constraints on tachyon models of dark energy. J. Cosmol. Astropart. Phys. 2019(04), 047 (2019)

    Article  Google Scholar 

  89. S.G. Shi, Y.S. Piao, C.F. Qiao, Cosmological evolution of a tachyon-quintom model of dark energy. J. Cosmol. Astropart. Phys. 2009(04), 027 (2009)

    Article  ADS  Google Scholar 

  90. A. Frolov, L. Kofman, A. Starobinsky, Prospects and problems of tachyon matter cosmology. Phys. Lett. B 545(1–2), 8–16 (2002)

    Article  ADS  MATH  Google Scholar 

  91. A. Feinstein, Power-law inflation from the rolling tachyon. Phys. Rev. D 66(6), 063511 (2002)

    Article  ADS  Google Scholar 

  92. J.M. Aguirregabiria, R. Lazkoz, Tracking solutions in tachyon cosmology. Phys. Rev. D 69(12), 123502 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  93. Z.K. Guo, Y.Z. Zhang, Cosmological scaling solutions of multiple tachyon fields with inverse square potentials. J. Cosmol. Astropart. Phys. 2004(08), 010 (2004)

    Article  Google Scholar 

  94. J.G. Hao, X.Z. Li, Phantom with Born–Infeld-type Lagrangian. Phys. Rev. D 68(4), 043501 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  95. A. Sheykhi, M.S. Movahed, E. Ebrahimi, Tachyon reconstruction of ghost dark energy. Astrophys. Space Sci. 339(1), 93–99 (2012)

    Article  ADS  MATH  Google Scholar 

  96. Y. Cai, Y. Wan, H.G. Li, T. Qiu, Y.S. Piao, The effective field theory of nonsingular cosmology. J. High Energy Phys. 2017(1), 90 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  97. V. Gorini, A. Kamenshchik, U. Moschella, V. Pasquier, A. Starobinsky, Stability properties of some perfect fluid cosmological models. Phys. Rev. D 72(10), 103518 (2005)

    Article  ADS  Google Scholar 

  98. H.B. Sandvik, M. Tegmark, M. Zaldarriaga, I. Waga, The end of unified dark matter? Phys. Rev. D 69(12), 123524 (2004)

    Article  ADS  Google Scholar 

  99. J.Q. Xia, Y.F. Cai, T.T. Qiu, G.B. Zhao, X. Zhang, Constraints on the sound speed of dynamical dark energy. Int. J. Mod. Phys. D 17(08), 1229–1243 (2008)

    Article  ADS  MATH  Google Scholar 

  100. H. Kodama, M. Sasaki, Cosmological perturbation theory. Prog. Theor. Phys. Suppl. 78, 1–166 (1984)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Gujrat, Gujrat, Pakistan

    Muhamad Zahid Mughal & Iftikhar Ahmad

Authors
  1. Muhamad Zahid Mughal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Iftikhar Ahmad
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Iftikhar Ahmad.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mughal, M.Z., Ahmad, I. A multi-field tachyon-quintom model of dark energy and fate of the universe. Eur. Phys. J. Plus 136, 581 (2021). https://doi.org/10.1140/epjp/s13360-021-01547-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-021-01547-0

Search

Navigation