Advertisement

Journal of the Korean Physical Society

, Volume 74, Issue 12, pp 1101–1111 | Cite as

Conformal Frame Dependence on Cosmological Observations in Scalar-Tensor Theories of Gravity

  • Young-Hwan Hyun
  • Yoonbai Kim
  • Seokcheon LeeEmail author
Article
  • 11 Downloads

Abstract

Cosmological observations provide more accurate values both for the background evolution of the Universe and for the structure formation. These values are given by the so-called dark energy equation of state, ω, and the growth index parameter, γ. From these observed parameters, one can reconstruct the model functions in scalar-tensor gravity theories. However, there is a long-standing debate about the (in)equality between conformally transformed frames in scalar-tensor gravity models and some cosmological observables have been shown to be frame independent and others frame dependent. We focus on the cosmological evolutions of the frame-dependent observables, which are functions of the frame-independent parameter, the redshift. Thus, if one measures the cosmological parameters ω and γ from the frame-dependent cosmological observables in one specific frame, then all of the other observables should also be interpreted in that frame with the same cosmological parameters obtained from that measurement. If one analyzes the same observables in another frame, then the obtained cosmological parameters should be different from those of the original frame. This explicitly shows the frame dependence of cosmological observables. Also, our method provides a model-independent analysis of scalar-tensor theories of gravity models about various observables in both frames.

Keywords

Conformal transformation Modified gravity theories Dark energy Cosmological observabales 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

Acknowledgments

Y.-H. Hyun, Y. Kim, and S. Lee are supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (Grant No. NRF-2018R1D1A1B07049514, NRF-2016R1 D1A1B03931090, and NRF-2017R1A2B4011168, respectively). Y.-H. Hyun is also supported by the Korea Institute of Science and Technology Information (K-19-L02-C07-S01).

References

  1. [1]
    S. Lee, Mod. Phys. Lett. A 23, 1388 (2008).ADSGoogle Scholar
  2. [2]
    M. Chevallier and D. Polarski, Int. J. Mod. Phys. D 10, 213 (2001).ADSGoogle Scholar
  3. [3]
    E.V. Linder, Phys. Rev. Lett. 90, 091301 (2003).ADSGoogle Scholar
  4. [4]
    M. Ishak, A. Upadhye and D.N. Spergel, Phys. Rev. D 74, 043513 (2006).ADSGoogle Scholar
  5. [5]
    M. Kunz and D. Sapone, Phys. Rev. Lett. 98, 121301 (2007).ADSGoogle Scholar
  6. [6]
    L. Amendola, M. Kunz and D. Sapone, J. Cosmol. Astropart. Phys. 0804, 013 (2008).ADSGoogle Scholar
  7. [7]
    I. Laszlo and R. Bean, Phys. Rev. D 77, 024048 (2008).ADSGoogle Scholar
  8. [8]
    E. Bertschinger and P. Zukin, Phys. Rev. D 78, 024015 (2008).ADSGoogle Scholar
  9. [9]
    S.F. Daniel, R.R. Caldwell, A. Cooray and A. Melchiorri, Phys. Rev. D 77, 103513 (2008).ADSGoogle Scholar
  10. [10]
    H. Wei and S.N. Zhang, Phys. Rev. D 78, 023011 (2008).ADSGoogle Scholar
  11. [11]
    S. Lee, J. Cosmol. Astropart. Phys. 1103, 021 (2011).ADSGoogle Scholar
  12. [12]
    S. Lee, J. Cosmol. Astropart. Phys. 1402, 021 (2014).ADSGoogle Scholar
  13. [13]
    S. Fay, Mon. Not. R. Astron. Soc. 460, 1863 (2016).ADSGoogle Scholar
  14. [14]
    S. Basilakos and S. Nesseris.Google Scholar
  15. [15]
    G. Dvali, G. Gabadadze and M. Porrati, Phys. Lett. B 485, 208 (2000).ADSMathSciNetGoogle Scholar
  16. [16]
    C. Deffayet, Phys. Lett. B 502, 199 (2001).ADSGoogle Scholar
  17. [17]
    C. Deffayet, G. Dvali and G. Gabadadze, Phys. Rev. D 65, 044023 (2002).ADSMathSciNetGoogle Scholar
  18. [18]
    A. Lue, R. Scoccimarro and G.D. Starkman, Phys. Rev. D 69, 124015 (2004).ADSGoogle Scholar
  19. [19]
    E. V. Linder and R.N. Cahn, Astropart. Phys. 28, 481 (2007).ADSGoogle Scholar
  20. [20]
    H. Wei, Phys. Lett. B 664, 1 (2008).ADSGoogle Scholar
  21. [21]
    X. Fu, P. Wu and H. Yu, Phys. Lett. B 677, 12 (2009).ADSGoogle Scholar
  22. [22]
    P. Wu, H. Yu and X. Fu, J. Cosmol. Astropart. Phys. 0906, 019 (2009).ADSGoogle Scholar
  23. [23]
    H.A. Buchdahl, Mon. Not. Roy. Astron. Soc. 150, 1 (1970).ADSGoogle Scholar
  24. [24]
    V. Acquaviva, A. Hajian, D. N. Spergel and S. Das, Phys. Rev. D 78, 043514 (2008).ADSGoogle Scholar
  25. [25]
    R. Gannouji, B. Moraes and D. Polarski, J. Cosmol. As-tropart. Phys. 0902, 034 (2010).ADSGoogle Scholar
  26. [26]
    J.B. Dent, S. Dutta and L. Perivolaropoulos, Phys. Rev. D 80, 023514 (2009).ADSGoogle Scholar
  27. [27]
    S. Tsujikawa, R. Gannouji, B. Moraes and D. Polarski, Phys. Rev. D 80, 084044 (2009).ADSGoogle Scholar
  28. [28]
    P.G. Bergmann, Int. J. Theor. Phys 1, 25 (1968).Google Scholar
  29. [29]
    K. Nordtvedt, Astrophys. J. 161, 1059 (1970).ADSMathSciNetGoogle Scholar
  30. [30]
    R. Wagoner, Phys. Rev. D 1, 3209 (1970).ADSGoogle Scholar
  31. [31]
    B. Boisseau, G. Esposito-Farese, D. Polarski and A.A. Starobinsky, Phys. Rev. Lett. 85, 2236 (2000).ADSGoogle Scholar
  32. [32]
    D. Polarski and R. Gannouji, Phys. Lett. B 660, 439 (2008).ADSGoogle Scholar
  33. [33]
    R. Gannouji and D. Polarski, J. Cosmol. Astropart. Phys. 0805, 018 (2008).ADSGoogle Scholar
  34. [34]
    E. S. Fradkin and A.A. Tseytlin, Nucl. Phys. B 261, 1 (1985).ADSGoogle Scholar
  35. [35]
    C.G. Callan, D. Friedan, E. J. Martinec and M.J. Perry, Nucl. Phys. B 262, 593 (1985).ADSGoogle Scholar
  36. [36]
    C. Lovelace, Nucl. Phys. B 273, 413 (1985).ADSMathSciNetGoogle Scholar
  37. [37]
    B. Green, J. M. Schwarz and E. Witten, Superstring Theory (Cambridge University Press, 1987).zbMATHGoogle Scholar
  38. [38]
    J. Polchinski, String Theory (Cambridge University Press, 1998).zbMATHGoogle Scholar
  39. [39]
    P. Teyssandier and P. Tourrenc, J. Math. Phys. 24, 2793 (1983).ADSMathSciNetGoogle Scholar
  40. [40]
    G. Magnano, M. Ferraris and M. Francaviglia, Gen. Rel. Grav. 19, 465 (1987).ADSGoogle Scholar
  41. [41]
    D. Wands, Class. Quant. Grav. 11, 269 (1994).ADSGoogle Scholar
  42. [42]
    T. Chiba, Phys. Lett. B 575, 1 (2003).ADSGoogle Scholar
  43. [43]
    M. Capone and M.L. Ruggiero, Class. Quant. Grav. 27, 125006 (2010).ADSGoogle Scholar
  44. [44]
    E.E. Flanagan, Phys. Rev. Lett. 92, 071101 (2004).ADSMathSciNetGoogle Scholar
  45. [45]
    T. Sotiriou, Class. Quant. Grav. 23, 5117 (2006).ADSGoogle Scholar
  46. [46]
    J. Larena, J.-M. Alimi and A. Serna, Astrophys. J. 658, 1 (2007).ADSGoogle Scholar
  47. [47]
    A. Coc, K.A. Olive, J.-P. Uzan and E. Vangioni, Phys. Rev. D 73, 083525 (2006).ADSGoogle Scholar
  48. [48]
    A. Coc, K.A. Olive, J.-P. Uzan and E. Vangioni, Phys. Rev. D 79, 103512 (2009).ADSGoogle Scholar
  49. [49]
    V. Acquaviva, C. Baccigalupi and F. Perrotta, Phys. Rev. D 70, 023515 (2004).ADSMathSciNetGoogle Scholar
  50. [50]
    C. Schimd, J.-P. Uzan and A. Riazuelo, Phys. Rev. D 71, 083512 (2005).ADSMathSciNetGoogle Scholar
  51. [51]
    F. Perrotta, C. Baccigalupi and S. Matarrese, Phys. Rev. D 61, 023507 (2000).ADSGoogle Scholar
  52. [52]
    T. Giannantonio, Y.-S. Song and K. Koyama, Phys. Rev. D 78, 044017 (2008).ADSGoogle Scholar
  53. [53]
    S. Lee, AIP Conf. Proc. 1059, 27 (2008).ADSGoogle Scholar
  54. [54]
    T. Giannantonio, M. Martinelli, A. Silvestri and A. Melchiorri, J. Cosmol. Astropart. Phys. 1004, 030 (2010).ADSGoogle Scholar
  55. [55]
    T. Chiba and M. Yamaguchi, J. Cosmol. Astropart. Phys. 1310, 040 (2013).ADSGoogle Scholar
  56. [56]
    L. Perivolaropoulos, J. Cosmol. Astropart. Phys. 0510, 001 (2005).ADSGoogle Scholar
  57. [57]
    R. Gannouji, D. Polarski, A. Ranquet and A.A. Starobinsky, J. Cosmol. Astropart. Phys. 0609, 016 (2006).ADSGoogle Scholar
  58. [58]
    S. Nesseris and L. Perivolaropoulos, J. Cosmol. Astropart. Phys. 0701, 018 (2007).ADSGoogle Scholar
  59. [59]
    G. Esposito-Farese, [arXiv:gr-qc/0011115].Google Scholar
  60. [60]
    A. Riazuelo and J.-P. Uzan, Phys. Rev. D 66, 023525 (2002).ADSGoogle Scholar
  61. [61]
    S. Tsujikawa, Phys. Rev. D 72, 083512 (2005).ADSGoogle Scholar
  62. [62]
    T. Faulkner, M. Tegmark, E. F. Bunn and Y. Mao, Phys. Rev. D 76, 063505 (2007).ADSMathSciNetGoogle Scholar
  63. [63]
    S. Capozziello, S. Nesseris and L. Perivolaropoulos, J. Cosmol. Astropart. Phys. 0712, 009 (2007).ADSGoogle Scholar
  64. [64]
    S. Tsujikawa et al., Phys. Rev. D 77, 103009 (2008).ADSGoogle Scholar
  65. [65]
    L. Jarv, P. Kuusk and M. Saal, Phys. Rev. D 81, 104007 (2010).ADSGoogle Scholar
  66. [66]
    L. Jarv, P. Kuusk and M. Saal, Phys. Lett. B 694, 1 (2010).ADSMathSciNetGoogle Scholar
  67. [67]
    B. Boisseau, [arXiv:1011.2915].Google Scholar
  68. [68]
    G. Magnano and L.M. Sokolowski, Phys. Rev. D 50, 5039 (1994).ADSMathSciNetGoogle Scholar
  69. [69]
    R. Dick, Gen. Rel. Grav. 30, 435 (1998).ADSGoogle Scholar
  70. [70]
    V. Faraoni and E. Gunzig, Int. J. Theor. Phys. 38, 217 (1999).Google Scholar
  71. [71]
    C. Armendariz-Picon, Phys. Rev. D 66, 064008 (2002).ADSMathSciNetGoogle Scholar
  72. [72]
    R. Catena, M. Pietroni and L. Scarabello, Phys. Rev. D 76, 084039 (2007).ADSMathSciNetGoogle Scholar
  73. [73]
    A. Bhadra, K. Sarkar, D. P. Datta and K.K. Nandi, Mod. Phys. Lett. A 22, 367 (2007).ADSGoogle Scholar
  74. [74]
    S. Capozziello, P. Martin-Moruno and C. Rubano, Phys. Lett. B 689, 117 (2010).ADSMathSciNetGoogle Scholar
  75. [75]
    N. Banerjee and B. Majumder, Phys. Lett. B 754, 129 (2016).ADSGoogle Scholar
  76. [76]
    F. Rondeau and B. Li, Phys. Rev. D 96, 124009 (2017).ADSMathSciNetGoogle Scholar
  77. [77]
    G. Esposito-Farèse and D. Polarski, Phys. Rev. D 63, 063504 (2001).ADSGoogle Scholar
  78. [78]
    B. L’Huillier, A. Shafieloo and H. Kim, Mon. Not. Roy. Astron. Soc. 476, 3263 (2018)ADSGoogle Scholar
  79. [79]
    J. Zheng et al., Mon. Not. Roy. Astron. Soc. 484, 442 (2019).ADSGoogle Scholar
  80. [80]
    B. Sagredo, J. S. Lafaurie and D. Sapone, [arXiv:180805660].Google Scholar

Copyright information

© The Korean Physical Society 2019

Authors and Affiliations

  1. 1.Korea Institute of Science and Technology Information (KISTI)DaejeonKorea
  2. 2.Department of Physics and Institute of Basic ScienceSungkyunkwan UniversitySuwonKorea

Personalised recommendations