Advertisement

Kinematic model-independent reconstruction of Palatini f(R) cosmology

  • Salvatore Capozziello
  • Rocco D’Agostino
  • Orlando LuongoEmail author
Research Article

Abstract

A kinematic treatment to trace out the form of f(R) cosmology, within the Palatini formalism, is discussed by only postulating the universe homogeneity and isotropy. To figure this out we build model-independent approximations of the luminosity distance through rational expansions. These approximants extend the Taylor convergence radii computed for usual cosmographic series. We thus consider both Padé and the rational Chebyshev polynomials. They can be used to accurately describe the universe late-time expansion history, providing further information on the thermal properties of all effective cosmic fluids entering the energy momentum tensor of Palatini’s gravity. To perform our numerical analysis, we relate the Palatini’s Ricci scalar with the Hubble parameter H and thus we write down a single differential equation in terms of the redshift z. Therefore, to bound f(R), we make use of the most recent outcomes over the cosmographic parameters obtained from combined data surveys. In particular our clue is to select two scenarios, i.e. (2, 2) Padé and (2, 1) Chebyshev approximations, since they well approximate the luminosity distance at the lowest possible order. We find that best analytical matches to the numerical solutions lead to \(f(R)=a+bR^n\) with free parameters given by the set \((a, b, n)=(-1.627, 0.866, 1.074)\) for (2, 2) Padé approximation, whereas \(f(R)=\alpha +\beta R^m\) with \((\alpha , \beta , m)=(-1.332, 0.749, 1.124)\) for (2, 1) rational Chebyshev approximation. Finally, our results are compared with the \(\Lambda \)CDM predictions and with previous studies in the literature. Slight departures from General Relativity are also discussed.

Keywords

Palatini gravity Cosmography Rational approximations 

Notes

Acknowledgements

This paper is based upon work from COST action CA15117 (CANTATA), supported by COST (European Cooperation in Science and Technology).

References

  1. 1.
    Perlmutter, S., et al.: Nature 391, 51 (1998)ADSCrossRefGoogle Scholar
  2. 2.
    Riess, A.G., et al.: Astron. J. 116, 1009 (1998)ADSCrossRefGoogle Scholar
  3. 3.
    Schmidt, B.P., et al.: Astrophys. J. 507, 46 (1998)ADSCrossRefGoogle Scholar
  4. 4.
    Eisenstein, D.J., Hu, W., Tegmark, M.: Astrophys. J. 504, L57 (1998)ADSCrossRefGoogle Scholar
  5. 5.
    Hinshaw, G., et al.: Astrophys. J. Suppl. Ser. 208, 19 (2013)ADSCrossRefGoogle Scholar
  6. 6.
    Ade, P.A.R., et al.: [Planck Collaboration]. Astron. Astrophys. 594, A13 (2016)Google Scholar
  7. 7.
    Haridasu, B.S., Lukovic, V.V., D’Agostino, R., Vittorio, N.: Astron. Astrophys. 600, L1 (2017)ADSCrossRefGoogle Scholar
  8. 8.
    Bamba, K., Capozziello, S., Nojiri, S., Odintsov, S.D.: Astrophys. Space Sci. 342, 155 (2012)ADSCrossRefGoogle Scholar
  9. 9.
    Joyce, A., Lombriser, L., Schmidt, F.: Annu. Rev. Nucl. Part. Sci. 66, 95 (2016)ADSCrossRefGoogle Scholar
  10. 10.
    Kleidis, K., Spyrou, N.K.: Entropy 18, 3 (2016)CrossRefGoogle Scholar
  11. 11.
    Sahni, V., Starobinsky, A.: Int. J. Mod. Phys. D 9, 373 (2000)ADSGoogle Scholar
  12. 12.
    Copeland, E.J., Sami, M., Tsujikawa, S.: Int. J. Mod. Phys. D 15, 1753 (2006)ADSCrossRefGoogle Scholar
  13. 13.
    Zlatev, I., Wang, L.M., Steinhardt, P.J.: Phys. Rev. Lett. 82, 896 (1999)ADSCrossRefGoogle Scholar
  14. 14.
    Weinberg, S.: Rev. Mod. Phys. 61, 1–23 (1989)ADSCrossRefGoogle Scholar
  15. 15.
    Peebles, P.J.E., Ratra, B.: Phys. Rev. D 37, 3406 (1988)ADSCrossRefGoogle Scholar
  16. 16.
    Padmanabhan, T.: Phys. Rev. D 66, 021301 (2002)ADSCrossRefGoogle Scholar
  17. 17.
    Singh, P., Sami, M., Dadhich, N.: Phys. Rev. D 68, 023522 (2003)ADSCrossRefGoogle Scholar
  18. 18.
    Chevallier, M., Polarski, D.: Int. J. Mod. Phys. D 10, 213 (2001)ADSCrossRefGoogle Scholar
  19. 19.
    Linder, E.: Phys. Rev. Lett. 90, 091301 (2003)ADSCrossRefGoogle Scholar
  20. 20.
    Jassal, H.K., Bagla, J.S., Padmanabhan, T.: Mon. Not. R. Astron. Soc. 356, L11 (2005)ADSCrossRefGoogle Scholar
  21. 21.
    Bento, M.C., Bertolami, O., Sen, A.A.: Phys. Rev. D 66, 043507 (2002)ADSCrossRefGoogle Scholar
  22. 22.
    Capozziello, S., D’Agostino, R., Luongo, O.: Phys. Dark Univ. 20, 1 (2018)CrossRefGoogle Scholar
  23. 23.
    Csaki, C., Graesser, M., Randall, L., Terning, J.: Phys. Rev. D 62, 045015 (2000)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    Maartens, R.: Liv. Rev. Rel. 7, 7 (2004)CrossRefGoogle Scholar
  25. 25.
    Sotiriou, T.P., Faraoni, V.: Rev. Mod. Phys. 82, 451 (2010)ADSCrossRefGoogle Scholar
  26. 26.
    Capozziello, S., De Laurentis, M.: Phys. Rep. 509, 167321 (2011)CrossRefGoogle Scholar
  27. 27.
    Nojiri, S., Odintsov, S.D., Oikonomou, V.K.: Phys. Rep. 692, 1 (2017)ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    Nojiri, S., Odintsov, S.D.: Phys. Rev. D 68, 123512 (2003)ADSCrossRefGoogle Scholar
  29. 29.
    Carroll, S.M., Duvvuri, V., Trodden, M., Turner, M.S.: Phys. Rev. D 70, 043528 (2004)ADSCrossRefGoogle Scholar
  30. 30.
    Olmo, G.J.: Phys. Rev. D 72, 083505 (2005)ADSCrossRefGoogle Scholar
  31. 31.
    Amendola, L., Polarski, D., Tsujikawa, S.: Phys. Rev. Lett. 98, 131302 (2007)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    Capozziello, S., Cardone, V.F., Carloni, S., Troisi, A.: Int. J. Mod. Phys. D 12, 1969 (2003)ADSCrossRefGoogle Scholar
  33. 33.
    Koivisto, T.: Phys. Rev. D 73, 083517 (2006)ADSCrossRefGoogle Scholar
  34. 34.
    Santos, J., Alcaniz, J.S., Carvalho, F.C., Pires, N.: Phys. Lett. B 669, 14 (2008)ADSCrossRefGoogle Scholar
  35. 35.
    Basilakos, S., Nesseris, S., Perivolaropoulos, L.: Phys. Rev. D 87, 123529 (2013)ADSCrossRefGoogle Scholar
  36. 36.
    Nunes, R.C., Pan, S., Saridakis, E.N., Abreu, E.M.C.: J. Cosmol. Astrop. Phys. 1701, 005 (2017)ADSCrossRefGoogle Scholar
  37. 37.
    Santos, B., Campista, M., Santos, J., Alcaniz, J.S.: Astron. Astrophys. 548, A31 (2012)ADSCrossRefGoogle Scholar
  38. 38.
    Campista, M., Santos, B., Santos, J., Alcaniz, J.S.: Phys. Lett. B 699, 320 (2011)ADSCrossRefGoogle Scholar
  39. 39.
    Capozziello, S., Cardone, Vincenzo F., Francaviglia, M.: Gen. Relativ. Gravit. 38, 711 (2006)ADSCrossRefGoogle Scholar
  40. 40.
    Fay, S., Tavakol, R., Tsujikawa, S.: Phys. Rev. D 75, 063509 (2007)ADSMathSciNetCrossRefGoogle Scholar
  41. 41.
    Tsujikawa, S., Uddin, K., Tavakol, R.: Phys. Rev. D 77, 043007 (2008)ADSMathSciNetCrossRefGoogle Scholar
  42. 42.
    Pires, N., Santos, J., Alcaniz, J.S.: Phys. Rev. D 82, 067302 (2010)ADSCrossRefGoogle Scholar
  43. 43.
    Capozziello, S., Cardone, V.F., Troisi, A.: Phys. Rev. D 71, 043503 (2005)ADSCrossRefGoogle Scholar
  44. 44.
    Capozziello, S., D’Agostino, R., Luongo, O.: J. Cosmol. Astrop. Phys. 1805, 008 (2018)ADSCrossRefGoogle Scholar
  45. 45.
    Gruber, C., Luongo, O.: Phys. Rev. D 89, 103506 (2014)ADSCrossRefGoogle Scholar
  46. 46.
    Aviles, A., Bravetti, A., Capozziello, S., Luongo, O.: Phys. Rev. D 90, 043531 (2014)ADSCrossRefGoogle Scholar
  47. 47.
    Capozziello, S., D’Agostino, R., Luongo, O.: Mon. Not. R. Astron. Soc. 476, 3924 (2018)ADSCrossRefGoogle Scholar
  48. 48.
    Capozziello, S., Ruchika Sen, A.A.: arXiv:1806.03943 [astro-ph.CO] (2018)
  49. 49.
    Capozziello, S.: Int. J. Mod. Phys. D 11, 483–492 (2002)ADSCrossRefGoogle Scholar
  50. 50.
    Allemandi, G., Borowiec, A., Francaviglia, M.: Phys. Rev. D 70, 103503 (2004)ADSCrossRefGoogle Scholar
  51. 51.
    Carloni, S., Dunsby, P.K.S., Capozziello, S., Troisi, A.: Class. Quant. Grav. 22, 4839 (2005)ADSCrossRefGoogle Scholar
  52. 52.
    Vollick, D.N.: Phys. Rev. D 68, 063510 (2003)ADSCrossRefGoogle Scholar
  53. 53.
    Will, C.M.: Theory and Experiment in Gravitational Physics. Cambridge University Press, New York (1981)Google Scholar
  54. 54.
    Saini, T.D., Raychaudhury, S., Sahni, V., Starobinsky, A.A.: Phys. Rev. Lett. 85, 1162 (2000)ADSCrossRefGoogle Scholar
  55. 55.
    Visser, M.: Class. Quantum Grav. 21, 2603 (2004)ADSCrossRefGoogle Scholar
  56. 56.
    Cattoen, C., Visser, M.: Class. Quantum Grav. 24, 5985 (2007)ADSCrossRefGoogle Scholar
  57. 57.
    Carvalho, J.C., Alcaniz, J.S.: Mon. Not. R. Astron. Soc. 418, 1873 (2011)ADSCrossRefGoogle Scholar
  58. 58.
    Luongo, O.: Mod. Phys. Lett. A 26, 1459 (2011)ADSCrossRefGoogle Scholar
  59. 59.
    Busti, V.C., et al.: Phys. Rev. D 92, 123512 (2015)ADSCrossRefGoogle Scholar
  60. 60.
    Aviles, A., Gruber, C., Luongo, O., Quevedo, H.: Phys. Rev. D 86, 123516 (2012)ADSCrossRefGoogle Scholar
  61. 61.
    Baker Jr., G.A., Graves-Morris, P.: Padé Approximants. Cambridge University Press, Cambridge (1996)CrossRefGoogle Scholar
  62. 62.
    Litvinov, G.: Appl. Russ. J. Math. Phys. 1, 313 (1993)Google Scholar
  63. 63.
    Gerald, C.F., Wheatley, P.O.: Applied Numerical Analysis. Prentice Hall College Div, New Jersey (2003)zbMATHGoogle Scholar
  64. 64.
    Obsieger, B.: Numerical Methods III—Approximations of Functions. University of Rijeka, Rijeka (2013)Google Scholar
  65. 65.
    Baghram, S., Rahvar, S.: Phys. Rev. D 80, 124049 (2009)ADSCrossRefGoogle Scholar
  66. 66.
    Dick, R.: Gen. Relativ. Gravit. 36, 217 (2004)ADSCrossRefGoogle Scholar
  67. 67.
    Dominguez, A.E., Barraco, D.E.: Phys. Rev. D 70, 043505 (2004)ADSCrossRefGoogle Scholar
  68. 68.
    Martins, C.J.A.P.: Rep. Prog. Phys. 80, 12 (2017)CrossRefGoogle Scholar
  69. 69.
    Hu, W., Sawicki, I.: Phys. Rev. D 76, 064004 (2007)ADSCrossRefGoogle Scholar
  70. 70.
    Appleby, S.A., Battye, R.A.: Phys. Lett. B 654, 7 (2007)ADSMathSciNetCrossRefGoogle Scholar
  71. 71.
    de la Cruz-Dombriz, A., Dunsby, P.K.S., Luongo, O., Reverberi, L.: J. Cosmol. Astrop. Phys. 1612, 042 (2016)CrossRefGoogle Scholar
  72. 72.
    Dunsby, P.K.S., Luongo, O.: Int. J. Geom. Method Mod. Phys. 13, 1630002 (2016)CrossRefGoogle Scholar
  73. 73.
    Basilakos, S., Nesseris, S., Perivolaropoulos, L.: Phys. Rev. D 87, 123529 (2013)ADSCrossRefGoogle Scholar
  74. 74.
    Pan, S., Chakraborty, S.: Int. J. Mod. Phys. D 23, 1450092 (2014)ADSCrossRefGoogle Scholar
  75. 75.
    Borowiec, A., Godlowski, W., Szydlowski, M.: Phys. Rev. D 74, 043502 (2006)ADSCrossRefGoogle Scholar
  76. 76.
    Amarzguioui, M., Elgaroy, O., Mota, D.F., Multamaki, T.: Astron. Astrophys. 454, 707 (2006)ADSCrossRefGoogle Scholar
  77. 77.
    Li, B., Chan, K.C., Chu, M.C.: Phys. Rev. D 76, 024002 (2007)ADSMathSciNetCrossRefGoogle Scholar
  78. 78.
    Carvalho, F.C., Santos, E.M., Alcaniz, J.S., Santos, J.: J. Cosmol. Astropart. Phys. 0809, 008 (2008)ADSCrossRefGoogle Scholar
  79. 79.
    Ruggiero, M. L.: [\(n\) Collaboration], Gen. Relativ. Gravit. 41, 1497 (2009)Google Scholar
  80. 80.
    Yang, X.J., Chen, D.M.: Mon. Not. R. Astron. Soc. 394, 1449 (2009)ADSCrossRefGoogle Scholar
  81. 81.
    Roshan, M., Shojai, F.: Phys. Lett. B 668, 238 (2008)ADSMathSciNetCrossRefGoogle Scholar
  82. 82.
    Capozziello, S., De Felice, A.: J. Cosmol. Astropart. Phys. 0808, 016 (2008)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Salvatore Capozziello
    • 1
    • 2
    • 3
  • Rocco D’Agostino
    • 4
    • 5
  • Orlando Luongo
    • 6
    • 7
    • 8
    Email author
  1. 1.Dipartimento di Fisica “E. Pancini”Università di Napoli “Federico II”NaplesItaly
  2. 2.Istituto Nazionale di Fisica Nucleare (INFN), Sez. di NapoliNaplesItaly
  3. 3.Gran Sasso Science InstituteL’AquilaItaly
  4. 4.Dipartimento di FisicaUniversità degli Studi di Roma “Tor Vergata”RomeItaly
  5. 5.Istituto Nazionale di Fisica Nucleare (INFN), Sez. di Roma “Tor Vergata”RomeItaly
  6. 6.Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di FrascatiFrascatiItaly
  7. 7.School of Science and TechnologyUniversity of CamerinoCamerinoItaly
  8. 8.Instituto de Ciencias NuclearesUniversidad Nacional Autonoma de MexicoMexicoMexico

Personalised recommendations