- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Approximation of the potential in scalar field dark energy models

Richard A. Battye† and Francesco Pace*

  • Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom

  • *Corresponding author. francesco.pace@manchester.ac.uk
  • †richard.battye@manchester.ac.uk
PDF

Phys. Rev. D 94, 063513 – Published 13 September, 2016

DOI: https://doi.org/10.1103/PhysRevD.94.063513

Abstract

We study the nature of potentials in scalar field based models for dark energy—with both canonical and noncanonical kinetic terms. We calculate numerically, and using an analytic approximation around a≈1, potentials for models with constant equation-of-state parameter wϕ. We find that for a wide range of models with canonical and noncanonical kinetic terms there is a simple approximation for the potential that holds when the scale factor is in the range 0.6≲a≲1.4. We discuss how this form of the potential can also be used to represent models with nonconstant wϕ and, hence, how it could be used in reconstruction from cosmological data.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (80)

  1. Planck Collaboration XIII, arXiv:1502.01589 [Astron. Astrophys. (to be published)].
  2. Planck Collaboration XIV, arXiv:1502.01590.
  3. L. H. Ford, Phys. Rev. D 35, 2339 (1987).
  4. P. J. E. Peebles and B. Ratra, Astrophys. J. Lett. 325, L17 (1988).
  5. B. Ratra and P. J. E. Peebles, Phys. Rev. D 37, 3406 (1988).
  6. C. Wetterich, Nucl. Phys. B302, 668 (1988).
  7. R. R. Caldwell, R. Dave, and P. J. Steinhardt, Phys. Rev. Lett. 80, 1582 (1998).
  8. E. J. Copeland, A. R. Liddle, and D. Wands, Phys. Rev. D 57, 4686 (1998).
  9. P. J. Steinhardt, L. Wang, and I. Zlatev, Phys. Rev. D 59, 123504 (1999).
  10. T. Barreiro, E. J. Copeland, and N. J. Nunes, Phys. Rev. D 61, 127301 (2000).
  11. C. Armendáriz-Picón, T. Damour, and V. Mukhanov, Phys. Lett. B 458, 209 (1999).
  12. T. Chiba, T. Okabe, and M. Yamaguchi, Phys. Rev. D 62, 023511 (2000).
  13. V. Mukhanov and A. Vikman, J. Cosmol. Astropart. Phys. 02 (2006) 004.
  14. M. Chevallier and D. Polarski, Int. J. Mod. Phys. D 10, 213 (2001).
  15. E. V. Linder, Phys. Rev. Lett. 90, 091301 (2003).
  16. http://www.euclid-ec.org/.
  17. R. Laureijs et al., arXiv:1110.3193.
  18. L. Amendola et al., Living Rev. Relativ. 16, 6 (2013).
  19. http://www.lsst.org.
  20. LSST Dark Energy Science Collaboration, arXiv:1211.0310.
  21. https://www.skatelescope.org/.
  22. P. Bull, S. Camera, A. Raccanelli, C. Blake, P. Ferreira, M. Santos, and D. J. Schwarz, arXiv:1501.04088.
  23. S. Camera, A. Raccanelli, P. Bull, D. Bertacca, X. Chen, P. Ferreira, M. Kunz, R. Maartens, Y. Mao, M. Santos, P. R. Shapiro, M. Viel, and Y. Xu, arXiv:1501.03851.
  24. A. Raccanelli, P. Bull, S. Camera, C. Blake, P. Ferreira, R. Maartens, M. Santos, P. Bull, D. Bacon, O. Doré, P. Ferreira, M. G. Santos, M. Viel, and G. B. Zhao, arXiv:1501.03821.
  25. M. G. Santos, P. Bull, D. Alonso, S. Camera, P. G. Ferreira, G. Bernardi, R. Maartens, M. Viel, F. Villaescusa-Navarro, F. B. Abdalla, M. Jarvis, R. B. Metcalf, A. Pourtsidou, and L. Wolz, arXiv:1501.03989.
  26. S. Hannestad and E. Mörtsell, J. Cosmol. Astropart. Phys. 09 (2004) 001.
  27. H. K. Jassal, J. S. Bagla, and T. Padmanabhan, Phys. Rev. D 72, 103503 (2005).
  28. E. M. Barboza and J. S. Alcaniz, Phys. Lett. B 666, 415 (2008).
  29. V. Sahni, A. Shafieloo, and A. A. Starobinsky, Phys. Rev. D 78, 103502 (2008).
  30. C. Zunckel and C. Clarkson, Phys. Rev. Lett. 101, 181301 (2008).
  31. U. Alam, V. Sahni, T. D. Saini, and A. A. Starobinsky, Mon. Not. R. Astron. Soc. 344, 1057 (2003).
  32. V. Sahni, T. D. Saini, A. A. Starobinsky, and U. Alam, JETP Lett. 77, 201 (2003).
  33. R. G. Crittenden, L. Pogosian, and G.-B. Zhao, J. Cosmol. Astropart. Phys. 12 (2009) 025.
  34. V. Sahni and A. Starobinsky, Int. J. Mod. Phys. D 15, 2105 (2006).
  35. M. Sahlén, A. R. Liddle, and D. Parkinson, Phys. Rev. D 72, 083511 (2005).
  36. I. J. Grivell and A. R. Liddle, Phys. Rev. D 61, 081301 (2000).
  37. E. J. Copeland, E. W. Kolb, A. R. Liddle, and J. E. Lidsey, Phys. Rev. D 48, 2529 (1993).
  38. R. A. Daly and S. G. Djorgovski, Astrophys. J. 597, 9 (2003).
  39. R. A. Daly and S. G. Djorgovski, Astrophys. J. 612, 652 (2004).
  40. J. Simon, L. Verde, and R. Jimenez, Phys. Rev. D 71, 123001 (2005).
  41. Z. Slepian, J. R. Gott, and J. Zinn, Mon. Not. R. Astron. Soc. 438, 1948 (2014).
  42. R. Crittenden, E. Majerotto, and F. Piazza, Phys. Rev. Lett. 98, 251301 (2007).
  43. T. Chiba, Phys. Rev. D 79, 083517 (2009).
  44. T. Chiba, Phys. Rev. D 80, 109902 (2009).
  45. T. Chiba, S. Dutta, and R. J. Scherrer, Phys. Rev. D 80, 043517 (2009).
  46. R. R. Caldwell, Phys. Lett. B 545, 23 (2002).
  47. G. F. R. Ellis and M. S. Madsen, Classical Quantum Gravity 8, 667 (1991).
  48. V. Sahni and A. Starobinsky, Int. J. Mod. Phys. D 9, 373 (2000).
  49. A. Paliathanasis, M. Tsamparlis, S. Basilakos, and J. D. Barrow, Phys. Rev. D 91, 123535 (2015).
  50. C. Armendariz-Picon, V. Mukhanov, and P. J. Steinhardt, Phys. Rev. Lett. 85, 4438 (2000).
  51. C. Armendariz-Picon, V. Mukhanov, and P. J. Steinhardt, Phys. Rev. D 63, 103510 (2001).
  52. T. Padmanabhan, Phys. Rev. D 66, 021301 (2002).
  53. L. P. Chimento, Phys. Rev. D 69, 123517 (2004).
  54. J. Garriga and V. F. Mukhanov, Phys. Lett. B 458, 219 (1999).
  55. E. J. Copeland, M. R. Garousi, M. Sami, and S. Tsujikawa, Phys. Rev. D 71, 043003 (2005).
  56. A. D. Rendall, Classical Quantum Gravity 23, 1557 (2006).
  57. J. De-Santiago, J. L. Cervantes-Cota, and D. Wands, Phys. Rev. D 87, 023502 (2013).
  58. J. De-Santiago and J. L. Cervantes-Cota, J. Phys. Conf. Ser. 485, 012017 (2014).
  59. M. Gasperini and G. Veneziano, Phys. Rep. 373, 1 (2003).
  60. L. R. Abramo and F. Finelli, Phys. Lett. B 575, 165 (2003).
  61. J. M. Aguirregabiria and R. Lazkoz, Phys. Rev. D 69, 123502 (2004).
  62. N. A. Hamed, H. S. Cheng, M. A. Luty, and S. Mukohyama, J. High Energy Phys. 05 (2004) 074.
  63. F. Piazza and S. Tsujikawa, J. Cosmol. Astropart. Phys. 07 (2004) 004.
  64. M. Alishahiha, E. Silverstein, and D. Tong, Phys. Rev. D 70, 123505 (2004).
  65. E. Silverstein and D. Tong, Phys. Rev. D 70, 103505 (2004).
  66. Z.-K. Guo and N. Ohta, J. Cosmol. Astropart. Phys. 04 (2008) 035.
  67. N. Bose and A. S. Majumdar, Phys. Rev. D 80, 103508 (2009).
  68. J. De-Santiago and J. L. Cervantes-Cota, Phys. Rev. D 83, 063502 (2011).
  69. M. Sharif, K. Yesmakhanova, S. Rani, and R. Myrzakulov, Eur. Phys. J. C 72, 2067 (2012).
  70. R. J. Scherrer, Phys. Rev. Lett. 93, 011301 (2004).
  71. A. Sen, Mod. Phys. Lett. A 17, 1797 (2002).
  72. A. Sen, J. High Energy Phys. 04 (2002) 048.
  73. A. Sen, Int. J. Mod. Phys. A 20, 5513 (2005).
  74. R.-J. Yang and S.-N. Zhang, Chin. Phys. Lett. 25, 344 (2008).
  75. R. Yang and J. Qi, Eur. Phys. J. C 72, 2095 (2012).
  76. R. Yang, B. Chen, J. Li, and J. Qi, Astrophys. Space Sci. 356, 399 (2015).
  77. A. A. Mamon and S. Das, Eur. Phys. J. C 75, 244 (2015).
  78. Z. Ossoulian, T. Golanbari, H. Sheikhahmadi, and K. Saaidi, Adv. High Energy Phys. 2016, 3047461 (2016).
  79. R. A. Battye, A. Moss, and J. A. Pearson, J. Cosmol. Astropart. Phys. 04 (2015) 048.
  80. F. Pace, C. Fedeli, L. Moscardini, and M. Bartelmann, Mon. Not. R. Astron. Soc. 422, 1186 (2012).

Outline

Information

Phys. Rev. D 94, 063513– Published 13 September, 2016
  • Received 9 July 2016

© 2016 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation