Improved Solar System bounds on the cosmologically viable \(f(\mathcal{G})\) gravity

Original Article
First Online:
Received:
Accepted:

Abstract

By making use of the supplementary advances of the perihelia provided by INPOP10a and INPOP15a (France) and EPM2011 (Russia) ephemerides, we obtain improved Solar System bounds on the cosmologically viable \(f(\mathcal{G})\) gravity, where \(f\) is an arbitrary function of the Gauss–Bonnet invariant \(\mathcal{G}\). When we estimate new bounds on its model parameters, we consider the Lense–Thirring effect caused by the Sun’s angular momentum and the uncertainty of the Sun’s quadrupole moment, neither of which were included in related works before. The bounds we obtain in the present work are tighter than the previous ones by at least 5 orders of magnitude.

Keywords

\(f(\mathcal{G})\) gravity Modified gravity Celestial mechanics Ephemeris 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgements

The work of X.-M.D. is funded by the National Natural Science Foundation of China (Grant Nos. 11473072, 11103085 and 11533004). The work of Y.X. is supported by the National Natural Science Foundation of China (Grant No. 11573015).

References

  1. Abdolmaleki, A., Najafi, T.: Int. J. Mod. Phys. D 25, 1650040 (2016) ADSCrossRefGoogle Scholar
  2. Adkins, G.S., McDonnell, J., Fell, R.N.: Phys. Rev. D 75(6), 064011 (2007) ADSMathSciNetCrossRefGoogle Scholar
  3. Alimohammadi, M., Ghalee, A.: Phys. Rev. D 80(4), 043006 (2009) ADSCrossRefGoogle Scholar
  4. Amendola, L., Charmousis, C., Davis, S.C.: J. Cosmol. Astropart. Phys. 12, 020 (2006) ADSCrossRefGoogle Scholar
  5. Amendola, L., Charmousis, C., Davis, S.C.: J. Cosmol. Astropart. Phys. 10, 004 (2007) ADSCrossRefGoogle Scholar
  6. Amendola, L., Charmousis, C., Davis, S.C.: Phys. Rev. D 78(8), 084009 (2008) ADSCrossRefGoogle Scholar
  7. Antoniadis, I., Rizos, J., Tamvakis, K.: Nucl. Phys. B 415, 497 (1994) ADSCrossRefGoogle Scholar
  8. Arakida, H.: Int. J. Theor. Phys. 52, 1408 (2013) MathSciNetCrossRefGoogle Scholar
  9. Bamba, K., Nojiri, S., Odintsov, S.D.: J. Cosmol. Astropart. Phys. 10, 045 (2008) ADSCrossRefGoogle Scholar
  10. Bamba, K., Odintsov, S.D., Sebastiani, L., Zerbini, S.: Eur. Phys. J. C 67, 295 (2010) ADSCrossRefGoogle Scholar
  11. Bamba, K., Makarenko, A.N., Myagky, A.N., Odintsov, S.D.: Phys. Lett. B 732, 349 (2014) ADSMathSciNetCrossRefGoogle Scholar
  12. Banijamali, A., Fazlpour, B.: Eur. Phys. J. C 71, 1684 (2011) ADSCrossRefGoogle Scholar
  13. Banijamali, A., Fazlpour, B.: Astrophys. Space Sci. 340, 399 (2012) ADSCrossRefGoogle Scholar
  14. Banijamali, A., Fazlpour, B., Setare, M.R.: Astrophys. Space Sci. 338, 327 (2012) ADSCrossRefGoogle Scholar
  15. Bazeia, D., Menezes, R., Petrov, A.Y.: Eur. Phys. J. C 58, 171 (2008) ADSCrossRefGoogle Scholar
  16. Bazeia, D., Lobão, A., Losano, L., Menezes, R., Petrov, A.Y.: Phys. Rev. D 92(6), 064010 (2015) ADSCrossRefGoogle Scholar
  17. Bell, J.F., Camilo, F., Damour, T.: Astrophys. J. 464, 857 (1996) ADSCrossRefGoogle Scholar
  18. Binétruy, P., Charmousis, C., Davis, S., Dufaux, J.-F.: Phys. Lett. B 544, 183 (2002) ADSMathSciNetCrossRefGoogle Scholar
  19. Bogdanos, C., Charmousis, C., Goutéraux, B., Zegers, R.: J. High Energy Phys. 10, 037 (2009) ADSCrossRefGoogle Scholar
  20. Böhmer, C.G., Lobo, F.S.N.: Phys. Rev. D 79(6), 067504 (2009) ADSCrossRefGoogle Scholar
  21. Bose, R.N., Modak, B.: Int. J. Theor. Phys. 51, 350 (2012) CrossRefGoogle Scholar
  22. Brevik, I., Quiroga, J.: Int. J. Mod. Phys. D 16, 817 (2007) ADSCrossRefGoogle Scholar
  23. Brustein, R., Madden, R.: Phys. Rev. D 57, 712 (1998) ADSCrossRefGoogle Scholar
  24. Canfora, F., Giacomini, A., Pavluchenko, S.A.: Phys. Rev. D 88(6), 064044 (2013) ADSCrossRefGoogle Scholar
  25. Capozziello, S., de Laurentis, M.: Phys. Rep. 509, 167 (2011) ADSMathSciNetCrossRefGoogle Scholar
  26. Capozziello, S., Francaviglia, M., Makarenko, A.N.: Astrophys. Space Sci. 349, 603 (2014) ADSCrossRefGoogle Scholar
  27. Capozziello, S., Makarenko, A.N., Odintsov, S.D.: Phys. Rev. D 87(8), 084037 (2013) ADSCrossRefGoogle Scholar
  28. Cardona, J.F., Tejeiro, J.M.: Astrophys. J. 493, 52 (1998) ADSCrossRefGoogle Scholar
  29. Cartier, C., Copeland, E.J., Madden, R.: J. High Energy Phys. 1, 035 (2000) ADSCrossRefGoogle Scholar
  30. Charmousis, C., Davis, S.C., Dufaux, J.-F.: J. High Energy Phys. 12, 029 (2003) ADSCrossRefGoogle Scholar
  31. Charmousis, C., Kolyvaris, T., Papantonopoulos, E., Tsoukalas, M.: J. High Energy Phys. 7, 85 (2014) ADSCrossRefGoogle Scholar
  32. Chattopadhyay, S.: Astrophys. Space Sci. 352, 937 (2014) ADSCrossRefGoogle Scholar
  33. Chattopadhyay, S., Ghosh, R.: Astrophys. Space Sci. 345, 11 (2013) ADSCrossRefGoogle Scholar
  34. Choudhury, S., SenGupta, S.: J. High Energy Phys. 02, 136 (2013) ADSCrossRefGoogle Scholar
  35. Clifton, T., Ferreira, P.G., Padilla, A., Skordis, C.: Phys. Rep. 513, 1 (2012) ADSMathSciNetCrossRefGoogle Scholar
  36. Cognola, G., Elizalde, E., Nojiri, S., Odintsov, S.D., Zerbini, S.: Phys. Rev. D 73(8), 084007 (2006) ADSCrossRefGoogle Scholar
  37. Cognola, G., Elizalde, E., Nojiri, S., Odintsov, S.D., Zerbini, S.: Phys. Rev. D 75(8), 086002 (2007) ADSMathSciNetCrossRefGoogle Scholar
  38. Damiani, C., Rozelot, J.P., Lefebvre, S., Kilcik, A., Kosovichev, A.G.: J. Atmos. Sol.-Terr. Phys. 73, 241 (2011) ADSCrossRefGoogle Scholar
  39. Damour, T., Esposito-Farèse, G.: Phys. Rev. D 53, 5541 (1996) ADSMathSciNetCrossRefGoogle Scholar
  40. Darabi, F.: Astrophys. Space Sci. 343, 499 (2013) ADSCrossRefGoogle Scholar
  41. Davis, S.C.: In: Rajantie, A., Contaldi, C., Dauncey, P., Stoica, H. (eds.) Particles, Strings, and Cosmology: 13th International Symposium on Particles, Strings, and Cosmology-PASCOS 2007. American Institute of Physics Conference Series, vol. 957, p. 379 (2007) Google Scholar
  42. De Felice, A., Suyama, T.: Prog. Theor. Phys. 125, 603 (2011) ADSCrossRefGoogle Scholar
  43. De Felice, A., Tanaka, T.: Prog. Theor. Phys. 124, 503 (2010) ADSCrossRefGoogle Scholar
  44. De Felice, A., Tsujikawa, S.: Phys. Lett. B 675, 1 (2009a) ADSCrossRefGoogle Scholar
  45. De Felice, A., Tsujikawa, S.: Phys. Rev. D 80(6), 063516 (2009b) ADSCrossRefGoogle Scholar
  46. De Felice, A., Gérard, J.-M., Suyama, T.: Phys. Rev. D 82(6), 063526 (2010a) ADSCrossRefGoogle Scholar
  47. De Felice, A., Mota, D.F., Tsujikawa, S.: Phys. Rev. D 81(2), 023532 (2010b) ADSCrossRefGoogle Scholar
  48. DeFelice, A., Mukherjee, P., Wang, Y.: Phys. Rev. D 77(2), 024017 (2008) ADSCrossRefGoogle Scholar
  49. De Felice, A., Suyama, T., Tanaka, T.: Phys. Rev. D 83(10), 104035 (2011) ADSCrossRefGoogle Scholar
  50. de la Cruz-Dombriz, Á., Sáez-Gómez, D.: Class. Quantum Gravity 29(24), 245014 (2012) ADSCrossRefGoogle Scholar
  51. De Laurentis, M., Paolella, M., Capozziello, S.: Phys. Rev. D 91(8), 083531 (2015) ADSMathSciNetCrossRefGoogle Scholar
  52. De Laurentis, M., De Rosa, R., Garufi, F., Milano, L.: Mon. Not. R. Astron. Soc. 424, 2371 (2012) ADSCrossRefGoogle Scholar
  53. Deng, X.-M.: Sci. China, Ser. G, Phys. Mech. Astron. 54, 2071 (2011) ADSCrossRefGoogle Scholar
  54. Deng, X.-M., Xie, Y.: Astrophys. Space Sci. 350, 103 (2014) ADSCrossRefGoogle Scholar
  55. Deng, X.-M., Xie, Y.: Eur. Phys. J. C 75, 539 (2015a) ADSCrossRefGoogle Scholar
  56. Deng, X.-M., Xie, Y.: New Astron. 35, 36 (2015b) ADSCrossRefGoogle Scholar
  57. Deng, X.-M., Xie, Y.: Ann. Phys. 361, 62 (2015c) ADSCrossRefGoogle Scholar
  58. Deng, X.-M., Xie, Y.: Int. J. Theor. Phys. 54, 1739 (2015d) CrossRefGoogle Scholar
  59. Deng, X.-M., Xie, Y.: Mod. Phys. Lett. A 31, 1650021 (2016a) ADSCrossRefGoogle Scholar
  60. Deng, X.-M., Xie, Y.: Phys. Rev. D 93(4), 044013 (2016b) ADSMathSciNetCrossRefGoogle Scholar
  61. Deng, X.-M., Xie, Y., Huang, T.-Y.: Phys. Rev. D 79(4), 044014 (2009) ADSCrossRefGoogle Scholar
  62. Dutta, M.K., Modak, B.: Int. J. Theor. Phys. 54, 2591 (2015) CrossRefGoogle Scholar
  63. Elizalde, E., Quiroga Hurtado, J., Arcos, H.I.: Int. J. Mod. Phys. D 17, 2159 (2008) ADSCrossRefGoogle Scholar
  64. Elizalde, E., Myrzakulov, R., Obukhov, V.V., Sáez-Gómez, D.: Class. Quantum Gravity 27(9), 095007 (2010) ADSCrossRefGoogle Scholar
  65. Escofet, A., Elizalde, E.: Mod. Phys. Lett. A 31, 1650108 (2016) ADSCrossRefGoogle Scholar
  66. Fayaz, V., Hossienkhani, H., Aghamohammadi, A.: Astrophys. Space Sci. 357, 136 (2015) ADSCrossRefGoogle Scholar
  67. Fienga, A., Laskar, J., Kuchynka, P., Le Poncin-Lafitte, C., Manche, H., Gastineau, M.: In: Klioner, S.A., Seidelmann, P.K., Soffel, M.H. (eds.) IAU Symposium, vol. 261, p. 159 (2009) Google Scholar
  68. Fienga, A., Laskar, J., Kuchynka, P., Manche, H., Desvignes, G., Gastineau, M., Cognard, I., Theureau, G.: Celest. Mech. Dyn. Astron. 111, 363 (2011) ADSCrossRefGoogle Scholar
  69. Fienga, A., Laskar, J., Exertier, P., Manche, H., Gastineau, M.: Celest. Mech. Dyn. Astron. 123, 325 (2015) ADSCrossRefGoogle Scholar
  70. Fienga, A., Laskar, J., Manche, H., Gastineau, M.: arXiv:1601.00947
  71. Freire, P.C.C., Wex, N.: Mon. Not. R. Astron. Soc. 409, 199 (2010) ADSCrossRefGoogle Scholar
  72. Freire, P.C.C., Kramer, M., Wex, N.: Class. Quantum Gravity 29(18), 184007 (2012) ADSCrossRefGoogle Scholar
  73. Gaete, M.B., Hassaïne, M.: Phys. Rev. D 88(10), 104011 (2013) ADSCrossRefGoogle Scholar
  74. Gannouji, R., Sami, M.: Phys. Rev. D 85(2), 024019 (2012) ADSCrossRefGoogle Scholar
  75. García, N.M., Harko, T., Lobo, F.S.N., Mimoso, J.P.: Phys. Rev. D 83(10), 104032 (2011a) ADSCrossRefGoogle Scholar
  76. García, N.M., Lobo, F.S.N., Mimoso, J.P., Harko, T.: J. Phys. Conf. Ser. 314(1), 012056 (2011b) CrossRefGoogle Scholar
  77. Gasperini, M., Veneziano, G.: Astropart. Phys. 1, 317 (1993) ADSCrossRefGoogle Scholar
  78. Gasperini, M., Maggiore, M., Veneziano, G.: Nucl. Phys. B 494, 315 (1997) ADSCrossRefGoogle Scholar
  79. Goheer, N., Goswami, R., Dunsby, P.K.S., Ananda, K.: Phys. Rev. D 79(12), 121301 (2009) ADSCrossRefGoogle Scholar
  80. Gorbunova, O., Sebastiani, L.: Gen. Relativ. Gravit. 42, 2873 (2010) ADSCrossRefGoogle Scholar
  81. Granda, L.N.: Mod. Phys. Lett. A 27, 1250018 (2012a) ADSCrossRefGoogle Scholar
  82. Granda, L.N.: Int. J. Theor. Phys. 51, 2813 (2012b) CrossRefGoogle Scholar
  83. Granda, L.N., Jimenez, D.F.: Phys. Rev. D 90(12), 123512 (2014) ADSCrossRefGoogle Scholar
  84. Granda, L.N., Loaiza, E.: Int. J. Mod. Phys. D 21, 1250002 (2012) ADSCrossRefGoogle Scholar
  85. Gross, D.J., Sloan, J.H.: Nucl. Phys. B 291, 41 (1987) ADSCrossRefGoogle Scholar
  86. Guo, Z.-K., Ohta, N., Tsujikawa, S.: Phys. Rev. D 75(2), 023520 (2007) ADSCrossRefGoogle Scholar
  87. Gürses, M.: Gen. Relativ. Gravit. 40, 1825 (2008) ADSCrossRefGoogle Scholar
  88. Hendi, S.H., Panahiyan, S., Eslam Panah, B., Faizal, M., Momennia, M.: Phys. Rev. D 94, 024028 (2016) ADSCrossRefGoogle Scholar
  89. Houndjo, M.J.S., Rodrigues, M.E., Momeni, D., Myrzakulov, R.: Can. J. Phys. 92, 1528 (2014) ADSCrossRefGoogle Scholar
  90. Iorio, L.: Astron. Astrophys. 431, 385 (2005a) ADSCrossRefGoogle Scholar
  91. Iorio, L.: Astron. Astrophys. 433, 385 (2005b) ADSCrossRefGoogle Scholar
  92. Iorio, L.: Int. J. Mod. Phys. D 15, 473 (2006) ADSMathSciNetCrossRefGoogle Scholar
  93. Iorio, L.: Found. Phys. 37, 897 (2007a) ADSCrossRefGoogle Scholar
  94. Iorio, L.: Astrophys. Space Sci. 312, 331 (2007b) ADSCrossRefGoogle Scholar
  95. Iorio, L.: Adv. Astron. 2008, 268647 (2008) ADSCrossRefGoogle Scholar
  96. Iorio, L.: New Astron. 14, 196 (2009a) ADSCrossRefGoogle Scholar
  97. Iorio, L.: Astron. J. 137, 3615 (2009b) ADSCrossRefGoogle Scholar
  98. Iorio, L.: Phys. Rev. D 84, 124001 (2011) ADSCrossRefGoogle Scholar
  99. Iorio, L.: Sol. Phys. 281, 815 (2012a) ADSCrossRefGoogle Scholar
  100. Iorio, L.: Celest. Mech. Dyn. Astron. 112, 117 (2012b) ADSCrossRefGoogle Scholar
  101. Iorio, L.: Gen. Relativ. Gravit. 44, 719 (2012c) ADSCrossRefGoogle Scholar
  102. Iorio, L.: Class. Quantum Gravity 30(16), 165018 (2013) ADSCrossRefGoogle Scholar
  103. Iorio, L.: Int. J. Mod. Phys. D 23, 1450006 (2014a) ADSCrossRefGoogle Scholar
  104. Iorio, L.: Class. Quantum Gravity 31(8), 085003 (2014b) ADSCrossRefGoogle Scholar
  105. Iorio, L.: Mon. Not. R. Astron. Soc. 444, 78 (2014c) ADSCrossRefGoogle Scholar
  106. Iorio, L.: Mon. Not. R. Astron. Soc. 437, 3482 (2014d) ADSCrossRefGoogle Scholar
  107. Iorio, L.: Astrophys. Space Sci. 362, 11 (2017) ADSCrossRefGoogle Scholar
  108. Iorio, L., Ruggiero, M.L.: Int. J. Mod. Phys. A 22, 5379 (2007) ADSCrossRefGoogle Scholar
  109. Iorio, L., Saridakis, E.N.: Mon. Not. R. Astron. Soc. 427, 1555 (2012) ADSCrossRefGoogle Scholar
  110. Iorio, L., Lichtenegger, H.I.M., Ruggiero, M.L., Corda, C.: Astrophys. Space Sci. 331, 351 (2011) ADSCrossRefGoogle Scholar
  111. Izaurieta, F., Rodríguez, E.: Class. Quantum Gravity 30(15), 155009 (2013) ADSCrossRefGoogle Scholar
  112. Jetzer, P., Sereno, M.: Phys. Rev. D 73(4), 044015 (2006) ADSCrossRefGoogle Scholar
  113. Kagramanova, V., Kunz, J., Lämmerzahl, C.: Phys. Lett. B 634, 465 (2006) ADSCrossRefGoogle Scholar
  114. Kanti, P., Gannouji, R., Dadhich, N.: Phys. Rev. D 92(8), 083524 (2015a) ADSMathSciNetCrossRefGoogle Scholar
  115. Kanti, P., Gannouji, R., Dadhich, N.: Phys. Rev. D 92(4), 041302 (2015b) ADSCrossRefGoogle Scholar
  116. Kawai, S., Soda, J.: Phys. Lett. B 460, 41 (1999) ADSCrossRefGoogle Scholar
  117. Kawai, S., Sakagami, M.-A., Soda, J.: Phys. Lett. B 437, 284 (1998) ADSMathSciNetCrossRefGoogle Scholar
  118. Kerr, A.W., Hauck, J.C., Mashhoon, B.: Class. Quantum Gravity 20, 2727 (2003) ADSCrossRefGoogle Scholar
  119. Koivisto, T., Mota, D.F.: Phys. Lett. B 644, 104 (2007a) ADSMathSciNetCrossRefGoogle Scholar
  120. Koivisto, T., Mota, D.F.: Phys. Rev. D 75(2), 023518 (2007b) ADSCrossRefGoogle Scholar
  121. Kozai, Y.: Astron. J. 64, 367 (1959) ADSMathSciNetCrossRefGoogle Scholar
  122. Kramer, M., Stairs, I.H., Manchester, R.N., McLaughlin, M.A., Lyne, A.G., Ferdman, R.D., Burgay, M., Lorimer, D.R., Possenti, A., D’Amico, N., Sarkissian, J.M., Hobbs, G.B., Reynolds, J.E., Freire, P.C.C., Camilo, F.: Science 314, 97 (2006) ADSCrossRefGoogle Scholar
  123. Kurmakaev, Z.K.: Sov. Astron. 15, 836 (1972) ADSMathSciNetGoogle Scholar
  124. Kusakabe, M., Koh, S., Kim, K.S., Cheoun, M.-K.: Phys. Rev. D 93(4), 043511 (2016) ADSMathSciNetCrossRefGoogle Scholar
  125. Lämmerzahl, C.: Sol. Syst. Res. 148, 501 (2009) Google Scholar
  126. Leith, B.M., Neupane, I.P.: J. Cosmol. Astropart. Phys. 5, 019 (2007) ADSCrossRefGoogle Scholar
  127. Lense, J., Thirring, H.: Phys. Z. Sowjetunion 19, 156 (1951) Google Scholar
  128. Li, B., Barrow, J.D., Mota, D.F.: Phys. Rev. D 76(4), 044027 (2007) ADSMathSciNetCrossRefGoogle Scholar
  129. Li, L.-S.: Astrophys. Space Sci. 327, 59 (2010) ADSCrossRefGoogle Scholar
  130. Li, L.-S.: Astrophys. Space Sci. 334, 125 (2011) ADSCrossRefGoogle Scholar
  131. Li, Z.-W., Yuan, S.-F., Lu, C., Xie, Y.: Res. Astron. Astrophys. 14, 139 (2014) ADSCrossRefGoogle Scholar
  132. Liang, S., Xie, Y.: Res. Astron. Astrophys. 14, 527 (2014) ADSCrossRefGoogle Scholar
  133. Liko, T.: Phys. Rev. D 77(6), 064004 (2008) ADSMathSciNetCrossRefGoogle Scholar
  134. Liu, M.-Y., Zhong, Z.-H., Han, Y.-C., Wang, X.-Y., Yang, Z.-S., Xie, Y.: Res. Astron. Astrophys. 14, 1019 (2014) ADSCrossRefGoogle Scholar
  135. Lu, C., Li, Z.-W., Yuan, S.-F., Wan, Z., Qin, S.-H., Zhu, K., Xie, Y.: Res. Astron. Astrophys. 14, 1301 (2014) ADSCrossRefGoogle Scholar
  136. Maeda, K.-I., Ohta, N.: Phys. Lett. B 597, 400 (2004) ADSMathSciNetCrossRefGoogle Scholar
  137. Makarenko, A.N., Obukhov, V.V., Kirnos, I.V.: Astrophys. Space Sci. 343, 481 (2013) ADSCrossRefGoogle Scholar
  138. Metsaev, R.R., Tseytlin, A.A.: Nucl. Phys. B 293, 385 (1987) ADSCrossRefGoogle Scholar
  139. Mišković, O., Olea, R.: Phys. Rev. D 79(12), 124020 (2009) ADSMathSciNetCrossRefGoogle Scholar
  140. Modak, B., Bose, R.N.: Int. J. Theor. Phys. 51, 2798 (2012) CrossRefGoogle Scholar
  141. Modak, B., Dutta, M.K.: Gen. Relativ. Gravit. 45, 91 (2013) ADSCrossRefGoogle Scholar
  142. Mohseni, M.: Phys. Lett. B 682, 89 (2009) ADSMathSciNetCrossRefGoogle Scholar
  143. Moldenhauer, J., Ishak, M., Thompson, J., Easson, D.A.: Phys. Rev. D 81(6), 063514 (2010) ADSCrossRefGoogle Scholar
  144. Myrzakulov, R., Sáez-Gómez, D., Tureanu, A.: Gen. Relativ. Gravit. 43, 1671 (2011) ADSCrossRefGoogle Scholar
  145. Myrzakulov, R., Sebastiani, L., Zerbini, S.: Gen. Relativ. Gravit. 45, 675 (2013) ADSCrossRefGoogle Scholar
  146. Neupane, I.P.: Class. Quantum Gravity 23, 7493 (2006) ADSMathSciNetCrossRefGoogle Scholar
  147. Nojiri, S., Odintsov, S.D.: Phys. Lett. B 631, 1 (2005) ADSMathSciNetCrossRefGoogle Scholar
  148. Nojiri, S., Odintsov, S.D., Gorbunova, O.G.: J. Phys. A, Math. Gen. 39, 6627 (2006) ADSCrossRefGoogle Scholar
  149. Nojiri, S., Odintsov, S.D., Sasaki, M.: Phys. Rev. D 71(12), 123509 (2005) ADSCrossRefGoogle Scholar
  150. Nojiri, S., Odintsov, S.D., Tretyakov, P.V.: Phys. Lett. B 651, 224 (2007) ADSMathSciNetCrossRefGoogle Scholar
  151. Nojiri, S., Odintsov, S.D., Tretyakov, P.V.: Prog. Theor. Phys. Suppl. 172, 81 (2008) ADSCrossRefGoogle Scholar
  152. Nozari, K., Rashidi, N.: Phys. Rev. D 88(8), 084040 (2013) ADSCrossRefGoogle Scholar
  153. Nozari, K., Aghabararian, R., Rashidi, N.: Astrophys. Space Sci. 358, 1 (2015) ADSCrossRefGoogle Scholar
  154. Nozari, K., Azizi, T., Setare, M.R.: J. Cosmol. Astropart. Phys. 10, 022 (2009) ADSCrossRefGoogle Scholar
  155. Odintsov, S.D., Oikonomou, V.K., Saridakis, E.N.: Ann. Phys. 363, 141 (2015) ADSCrossRefGoogle Scholar
  156. Odintsov, S.D., Oikonomou, V.K.: Phys. Lett. B 760, 259 (2016) ADSCrossRefGoogle Scholar
  157. Oikonomou, V.K.: Phys. Rev. D 92(12), 124027 (2015) ADSMathSciNetCrossRefGoogle Scholar
  158. Oikonomou, V.K.: Astrophys. Space Sci. 361, 211 (2016) ADSCrossRefGoogle Scholar
  159. Oliveros, A., Solis, E.L., Acero, M.A.: Mod. Phys. Lett. A 31, 1650009 (2016) ADSCrossRefGoogle Scholar
  160. Pani, P., Cardoso, V.: Phys. Rev. D 79(8), 084031 (2009) ADSCrossRefGoogle Scholar
  161. Pani, P., Berti, E., Cardoso, V., Read, J.: Phys. Rev. D 84(10), 104035 (2011) ADSCrossRefGoogle Scholar
  162. Pavluchenko, S.A.: Phys. Rev. D 94, 024046 (2016) ADSCrossRefGoogle Scholar
  163. Perlmutter, S., Aldering, G., Goldhaber, G., Knop, R.A., Nugent, P., Castro, P.G., Deustua, S., Fabbro, S., Goobar, A., Groom, D.E., Hook, I.M., Kim, A.G., Kim, M.Y., Lee, J.C., Nunes, N.J., Pain, R., Pennypacker, C.R., Quimby, R., Lidman, C., Ellis, R.S., Irwin, M., McMahon, R.G., Ruiz-Lapuente, P., Walton, N., Schaefer, B., Boyle, B.J., Filippenko, A.V., Matheson, T., Fruchter, A.S., Panagia, N., Newberg, H.J.M., Couch, W.J.: Astrophys. J. 517, 565 (1999) ADSCrossRefGoogle Scholar
  164. Pijpers, F.P.: Astron. Astrophys. 402, 683 (2003) ADSCrossRefGoogle Scholar
  165. Pireaux, S., Rozelot, J.-P.: Astrophys. Space Sci. 284, 1159 (2003) ADSCrossRefGoogle Scholar
  166. Pitjev, N.P., Pitjeva, E.V.: Astron. Lett. 39, 141 (2013) ADSCrossRefGoogle Scholar
  167. Pitjeva, E.V.: Sol. Syst. Res. 47, 386 (2013) ADSCrossRefGoogle Scholar
  168. Pitjeva, E.V., Pitjev, N.P.: Mon. Not. R. Astron. Soc. 432, 3431 (2013) ADSCrossRefGoogle Scholar
  169. Ragos, O., Haranas, I., Gkigkitzis, I.: Astrophys. Space Sci. 345, 67 (2013) ADSCrossRefGoogle Scholar
  170. Rastkar, A.R., Setare, M.R., Darabi, F.: Astrophys. Space Sci. 337, 487 (2012) ADSCrossRefGoogle Scholar
  171. Renzetti, G.: J. Astrophys. Astron. 34(4), 341 (2013) ADSCrossRefGoogle Scholar
  172. Renzetti, G.: Astrophys. Space Sci. 352, 493 (2014) ADSCrossRefGoogle Scholar
  173. Riess, A.G., Filippenko, A.V., Challis, P., Clocchiatti, A., Diercks, A., Garnavich, P.M., Gilliland, R.L., Hogan, C.J., Jha, S., Kirshner, R.P., Leibundgut, B., Phillips, M.M., Reiss, D., Schmidt, B.P., Schommer, R.A., Smith, R.C., Spyromilio, J., Stubbs, C., Suntzeff, N.B., Tonry, J.: Astron. J. 116, 1009 (1998) ADSCrossRefGoogle Scholar
  174. Rindler, W.: Relativity: Special, General, and Cosmological, 2nd edn. Oxford University Press, Oxford (2006) MATHGoogle Scholar
  175. Roberts, M.S., Whitehurst, R.N.: Astrophys. J. 201, 327 (1975) ADSCrossRefGoogle Scholar
  176. Rodrigues, D.C., Mauro, S., de Almeida, Á.O.F.: Phys. Rev. D 94(8), 084036 (2016) ADSCrossRefGoogle Scholar
  177. Rosa, V.M., Letelier, P.S.: Phys. Rev. D 78(8), 084038 (2008) ADSMathSciNetCrossRefGoogle Scholar
  178. Rozelot, J.-P., Damiani, C.: Eur. Phys. J. H 36, 407 (2011) CrossRefGoogle Scholar
  179. Rozelot, J.P., Fazel, Z.: Sol. Phys. 287, 161 (2013) ADSCrossRefGoogle Scholar
  180. Rozelot, J., Pireaux, S., Lefebvre, S., Corbard, T.: arXiv:astro-ph/0403382
  181. Rubin, V.C., Ford, W.K. Jr.: Astrophys. J. 159, 379 (1970) ADSCrossRefGoogle Scholar
  182. Rudra, P.: Int. J. Mod. Phys. D 24, 1550013 (2015) ADSCrossRefGoogle Scholar
  183. Sadeghi, J., Banijamali, A., Vaez, H.: Int. J. Theor. Phys. 51, 2888 (2012) CrossRefGoogle Scholar
  184. Sadeghi, J., Setare, M.R., Banijamali, A., Milani, F.: Phys. Rev. D 79(12), 123003 (2009) ADSCrossRefGoogle Scholar
  185. Sadjadi, H.M.: Phys. Scr. 83(5), 055006 (2011) ADSCrossRefGoogle Scholar
  186. Saltas, I.D., Kunz, M.: Phys. Rev. D 83(6), 064042 (2011) ADSCrossRefGoogle Scholar
  187. Sami, M., Toporensky, A., Tretjakov, P., Tsujikawa, S.: Phys. Lett. B 619, 193 (2005) ADSCrossRefGoogle Scholar
  188. Sanyal, A.K.: Phys. Lett. B 645, 1 (2007) ADSCrossRefGoogle Scholar
  189. Sanyal, A.K.: Gen. Relativ. Gravit. 41, 1511 (2009) ADSCrossRefGoogle Scholar
  190. Sanyal, A.K., Rubano, C., Piedipalumbo, E.: Gen. Relativ. Gravit. 43, 2807 (2011) ADSCrossRefGoogle Scholar
  191. Saridakis, E.N.: Phys. Lett. B 661, 335 (2008) ADSMathSciNetCrossRefGoogle Scholar
  192. Setare, M.R., Sadeghi, J., Banijamali, A.: Eur. Phys. J. C 64, 433 (2009) ADSCrossRefGoogle Scholar
  193. Shao, L.: Phys. Rev. Lett. 112(11), 111103 (2014) ADSCrossRefGoogle Scholar
  194. Shao, L., Wex, N.: Class. Quantum Gravity 29(21), 215018 (2012) ADSCrossRefGoogle Scholar
  195. Shao, L., Wex, N.: Class. Quantum Gravity 30(16), 165020 (2013) ADSCrossRefGoogle Scholar
  196. Shao, L., Caballero, R.N., Kramer, M., Wex, N., Champion, D.J., Jessner, A.: Class. Quantum Gravity 30(16), 165019 (2013) ADSCrossRefGoogle Scholar
  197. Sharif, M., Abbas, G.: J. Phys. Soc. Jpn. 82(3), 034006 (2013) ADSCrossRefGoogle Scholar
  198. Sharif, M., Fatima, H.I.: Mod. Phys. Lett. A 30, 1550142 (2015) ADSCrossRefGoogle Scholar
  199. Sharif, M., Ikram, A.: Int. J. Mod. Phys. D 24, 1550003 (2015) ADSCrossRefGoogle Scholar
  200. Sharif, M., Ismat Fatima, H.: Astrophys. Space Sci. 354, 507 (2014) ADSGoogle Scholar
  201. Sofue, Y., Rubin, V.: Annu. Rev. Astron. Astrophys. 39, 137 (2001) ADSCrossRefGoogle Scholar
  202. Sotiriou, T., Barausse, E.: Phys. Rev. D 75(8), 084007 (2007) ADSMathSciNetCrossRefGoogle Scholar
  203. Taj, S., Quevedo, H., Sánchez, A.: Gen. Relativ. Gravit. 44, 1489 (2012) ADSCrossRefGoogle Scholar
  204. Taves, T., Leonard, C.D., Kunstatter, G., Mann, R.B.: Class. Quantum Gravity 29(1), 015012 (2012) ADSCrossRefGoogle Scholar
  205. Tsujikawa, S.: Phys. Lett. B 526, 179 (2002) ADSCrossRefGoogle Scholar
  206. Tsujikawa, S., Sami, M.: J. Cosmol. Astropart. Phys. 1, 006 (2007) ADSCrossRefGoogle Scholar
  207. Tsujikawa, S., Brandenberger, R., Finelli, F.: Phys. Rev. D 66(8), 083513 (2002) ADSCrossRefGoogle Scholar
  208. Uddin, K., Lidsey, J.E., Tavakol, R.: Gen. Relativ. Gravit. 41, 2725 (2009) ADSCrossRefGoogle Scholar
  209. Verma, A.K., Fienga, A., Laskar, J., Manche, H., Gastineau, M.: Astron. Astrophys. 561, 115 (2014) ADSCrossRefGoogle Scholar
  210. Wongjun, P.: Eur. Phys. J. C 75, 6 (2015) ADSCrossRefGoogle Scholar
  211. Xie, Y.: Res. Astron. Astrophys. 13, 1 (2013) ADSCrossRefGoogle Scholar
  212. Xie, Y., Deng, X.-M.: Mon. Not. R. Astron. Soc. 433, 3584 (2013) ADSCrossRefGoogle Scholar
  213. Xie, Y., Deng, X.-M.: Mon. Not. R. Astron. Soc. 438, 1832 (2014) ADSCrossRefGoogle Scholar
  214. Yagi, K.: Phys. Rev. D 86(8), 081504 (2012) ADSCrossRefGoogle Scholar
  215. Yagi, K., Stein, L.C., Yunes, N., Tanaka, T.: Phys. Rev. D 87(8), 084058 (2013) ADSCrossRefGoogle Scholar
  216. Yagi, K., Blas, D., Barausse, E., Yunes, N.: Phys. Rev. D 89(8), 084067 (2014) ADSCrossRefGoogle Scholar
  217. Zhao, S.-S., Xie, Y.: Phys. Rev. D 92(6), 064033 (2015) ADSCrossRefGoogle Scholar
  218. Zhao, Y.-Y., Wu, Y.-B., Lu, J.-B., Zhang, Z., Han, W.-L., Lin, L.-L.: Eur. Phys. J. C 72, 1924 (2012) ADSCrossRefGoogle Scholar
  219. Zhou, S.-Y., Copeland, E.J., Saffin, P.M.: J. Cosmol. Astropart. Phys. 7, 009 (2009) ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Purple Mountain ObservatoryChinese Academy of SciencesNanjingChina
  2. 2.School of Astronomy and Space ScienceNanjing UniversityNanjingChina
  3. 3.Key Laboratory of Modern Astronomy and Astrophysics, Nanjing UniversityMinistry of EducationNanjingChina

Personalised recommendations