Reconstruction of dynamical dark energy potentials: Quintessence, tachyon and interacting models

  • Manvendra Pratap RajvanshiEmail author
  • J. S. Bagla


Dynamical models for dark energy are an alternative to the cosmological constant. It is important to investigate properties of perturbations in these models and go beyond the smooth FRLW cosmology. This allows us to distinguish different dark energy models with the same expansion history. For this, one often needs the potential for a particular expansion history. We study how such potentials can be reconstructed by obtaining closed formulae for potential or reducing the problem to quadrature. We consider three classes of models here: tachyons, quintessence and interacting dark energy. We present results for the constant w and the CPL parametrization. The method given here can be generalized to any arbitrary form of w(z).


Cosmology: dark energy theory 



The authors thank Dr. Ankan Mukherjee, Dr. H. K. Jassal, Dr. Varadharaj Srinivasan and Avinash Singh for useful discussions. This research has made use of NASA’s Astrophysics Data System Bibliographic Services.


  1. Agrawal P., Obied G., Steinhardt P. J., Vafa C. 2018, Phys. Lett. B, 784, 271, arXiv:1806.09718 [hep-th]ADSCrossRefGoogle Scholar
  2. Akrami Y., Kallosh R., Linde A., Vardanyan V. 2019, Fortsch. Phys., 67(1-2), 1800075, arXiv:1808.09440 [hep-th]CrossRefGoogle Scholar
  3. Amendola L., Tsujikawa S. 2010, Dark Energy: Theory and Observations, Cambridge University Press, CambridgeCrossRefGoogle Scholar
  4. Antia H. 2012, Numerical Methods for Scientists and Engineers, Hindustan Book Agency, New DelhiCrossRefGoogle Scholar
  5. Bagla J. S., Padmanabhan T., Narlikar J. V. 1996, Commun. Astrophys., 18, 275ADSGoogle Scholar
  6. Bagla J. S., Jassal H. K., Padmanabhan T. 2003, Phys. Rev. D, 67, 063504ADSCrossRefGoogle Scholar
  7. Bamba K., Capozziello S., Nojiri S., Odintsov S. D. 2012, Astrophys. Space Sci., 342, 155, arXiv:1205.3421 [gr-qc]ADSCrossRefGoogle Scholar
  8. Barros B. J., Amendola L., Barreiro T., Nunes N. J. 2018, Coupled quintessence with a \(\Lambda \)CDM background: Removing the \(\sigma \)\_8 tension, arXiv e-prints, February 2018Google Scholar
  9. Battye R. A., Pace F. 2016, Phys. Rev. D, 94(6), 063513, arXiv:1607.01720 [astro-ph.CO]ADSCrossRefGoogle Scholar
  10. Caldwell R. R., Dave R., Steinhardt P. J. 1998, Phys. Rev. Lett., 80, 1582ADSCrossRefGoogle Scholar
  11. Chevallier M., Polarski D. 2001, Int. J. Mod. Phys. D, 10, 213, arXiv:gr-qc/0009008 ADSCrossRefGoogle Scholar
  12. Clarkson C., Zunckel C. 2010, Phys. Rev. Lett., 104, 211301, arXiv:1002.5004 [astro-ph.CO]ADSCrossRefGoogle Scholar
  13. De Bernardis F., Martinelli M., Melchiorri A., Mena O., Cooray A. 2011, Phys. Rev. D, 84, 023504, arXiv:1104.0652 [astro-ph.CO]ADSCrossRefGoogle Scholar
  14. Durrer R. 2011, Philos. Trans. R. Soc. A, 369. ADSMathSciNetCrossRefGoogle Scholar
  15. Efstathiou G., Sutherland W. J., Maddox S. J. 1990, Nature, 348, 705ADSCrossRefGoogle Scholar
  16. Gerke B. F., Efstathiou G. 2002, Mon. Not. R. Astron. Soc., 335(1), 33ADSCrossRefGoogle Scholar
  17. Heisenberg L., Bartelmann M., Brandenberger R., Refregier A. 2018, Phys. Rev. D, 98(12), 123502, arXiv:1808.02877 [astro-ph.CO]ADSMathSciNetCrossRefGoogle Scholar
  18. Huterer D., Turner M. S. 1999, PRD, 60, 081301ADSCrossRefGoogle Scholar
  19. Huterer D., Shafer D. L. 2018, Rep. Prog. Phys., 81(1), 016901, arXiv:1709.01091 [astro-ph.CO]ADSCrossRefGoogle Scholar
  20. Jassal H. K. 2012, Phys. Rev. D, 86, 043528, arXiv:1203.5171 [astro-ph.CO]ADSCrossRefGoogle Scholar
  21. Li C., Holz D. E., Cooray A. 2007, PRD, 75, 103503ADSCrossRefGoogle Scholar
  22. Mifsud J., Van De Bruck C. 2017, JCAP, 1711(11), 001, arXiv:1707.07667 [astro-ph.CO]ADSCrossRefGoogle Scholar
  23. Ostriker J. P., Steinhardt P. J. 1995, Nature, 377, 600ADSCrossRefGoogle Scholar
  24. Padmanabhan T. 2002, Phys. Rev. D,, 66(2), 021301ADSCrossRefGoogle Scholar
  25. Pearson J. W. 2009, Computation of hypergeometric functions, Ph.D. thesis, 2009Google Scholar
  26. Perlmutter S., Aldering G., Goldhaber G. et al. 1999, ApJ, 517, 565ADSCrossRefGoogle Scholar
  27. Pettorino V., Baccigalupi C. 2008, Phys. Rev. D, 77, 103003, arXiv:0802.1086 [astro-ph]ADSCrossRefGoogle Scholar
  28. Rajvanshi M. P., Bagla J. S. 2018, JCAP, 1806(06), 018, arXiv:1802.05840 [astro-ph.CO]CrossRefGoogle Scholar
  29. Riess A. G., Filippenko A. V.,  Challis P. et al. 1998, AJ, 116, 1009ADSCrossRefGoogle Scholar
  30. Sahni V., Starobinsky A. 2006, Int. J. Mod. Phys. D, 15, 2105, arXiv:astro-ph/0610026 ADSCrossRefGoogle Scholar
  31. Saini T. D., Raychaudhury S., Sahni V., Starobinsky A. A. 2000, Phys. Rev. Lett., 85, 1162, arXiv:astro-ph/9910231 ADSCrossRefGoogle Scholar
  32. Sangwan A., Mukherjee A., Jassal H. K. 2010, JCAP, 1, 018ADSGoogle Scholar
  33. Scherrer R. J. 2015, Phys. Rev. D, 92(4), 043001 arXiv:1505.05781 [astro-ph.CO]ADSCrossRefGoogle Scholar
  34. Shahalam M., Pathak S. D., Verma M. M., Khlopov M. Y., Myrzakulov R. 2015, Eur. Phys. J. C, 75(8), 395, arXiv:1503.08712 [gr-qc]ADSCrossRefGoogle Scholar
  35. Tripathi A., Sangwan A., Jassal H. K. 2017, JCAP, 1706(06), 012, arXiv:1611.01899 [astro-ph.CO]ADSCrossRefGoogle Scholar
  36. Tsujikawa S. 2013, Class. Quantum Gravit., 30(21), 214003ADSCrossRefGoogle Scholar
  37. Wang Y. T., Xu L. X., Gui Y. X. 2010, Phys. Rev. D, 82, 083522, ADSCrossRefGoogle Scholar
  38. Weisstein E. W. 2018, Incomplete beta function, from mathworld—a wolfram web resource., accessed: 2018-10-15
  39. Yang W., Li H., Wu Y., Lu J. 2016, JCAP, 1610(10), 007, arXiv:1608.07039 [astro-ph.CO]ADSCrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  1. 1.Indian Institute of Science Education and Research MohaliSahibzada Ajit Singh NagarIndia

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