Reconstruction of the equation of state for the cyclic universes in homogeneous and isotropic cosmology

• Authors: Kazuharu Bamba , Kuralay Yesmakhanova , Koblandy Yerzhanov , Ratbay Myrzakulov
• Languages of publication: EN

Abstracts

EN

We study the cosmological evolutions of the equation of state (EoS) for the universe in the homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) space-time. In particular, we reconstruct the cyclic universes by using the Weierstrass and Jacobian elliptic functions. It is explicitly illustrated that in several models the universe always stays in the non-phantom (quintessence) phase, whereas there also exist models in which the crossing of the phantom divide can be realized in the reconstructed cyclic universes.

Keywords

EN

dark energy; cosmology

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2013
• Volume: 11
• Issue: 4
• Pages: 397-411

Dates

published

1 - 4 - 2013

online

22 - 5 - 2013

Contributors

author

Kazuharu Bamba

author

Kuralay Yesmakhanova

• Eurasian International Center for Theoretical Physics, Eurasian National University, Astana, 010008, Kazakhstan

author

Koblandy Yerzhanov

• Eurasian International Center for Theoretical Physics, Eurasian National University, Astana, 010008, Kazakhstan

author

Ratbay Myrzakulov

• Eurasian International Center for Theoretical Physics, Eurasian National University, Astana, 010008, Kazakhstan

References

• [1] D. N. Spergel et al. [WMAP Collaboration], Astrophys. J. Suppl. 148, 175 (2003) http://dx.doi.org/10.1086/377226[Crossref]
• [2] D. N. Spergel et al. [WMAP Collaboration], Astrophys. J. Suppl. 170, 377 (2007) http://dx.doi.org/10.1086/513700[Crossref]
• [3] E. Komatsu et al. [WMAP Collaboration], Astrophys. J. Suppl. 180, 330 (2009) http://dx.doi.org/10.1088/0067-0049/180/2/330[Crossref]
• [4] E. Komatsu et al. [WMAP Collaboration], Astrophys. J. Suppl. 192, 18 (2011) http://dx.doi.org/10.1088/0067-0049/192/2/18[Crossref]
• [5] G. Hinshaw et al., arXiv:1212.5226 [astro-ph.CO]
• [6] S. Perlmutter et al. [SNCP Collaboration], Astrophys. J. 517, 565 (1999) http://dx.doi.org/10.1086/307221[Crossref]
• [7] A. G. Riess et al. [Supernova Search Team Collaboration], Astron. J. 116, 1009 (1998) http://dx.doi.org/10.1086/300499[Crossref]
• [8] M. Tegmark et al. [SDSS Collaboration], Phys. Rev. D 69, 103501 (2004) http://dx.doi.org/10.1103/PhysRevD.69.103501[Crossref]
• [9] U. Seljak et al. [SDSS Collaboration], Phys. Rev. D 71, 103515 (2005) http://dx.doi.org/10.1103/PhysRevD.71.103515[Crossref]
• [10] D. J. Eisenstein et al. [SDSS Collaboration], Astrophys. J. 633, 560 (2005) http://dx.doi.org/10.1086/466512[Crossref]
• [11] B. Jain, A. Taylor, Phys. Rev. Lett. 91, 141302 (2003) http://dx.doi.org/10.1103/PhysRevLett.91.141302[Crossref]
• [12] E. J. Copeland, M. Sami, S. Tsujikawa, Int. J. Mod. Phys. D 15, 1753 (2006) http://dx.doi.org/10.1142/S021827180600942X[Crossref]
• [13] R. Durrer, R. Maartens, Gen. Rel. Grav. 40, 301 (2008) http://dx.doi.org/10.1007/s10714-007-0549-5[Crossref]
• [14] R. Durrer, R. Maartens, arXiv:0811.4132 [astro-ph]
• [15] Y. F. Cai, E. N. Saridakis, M. R. Setare, J. Q. Xia, Phys. Rept. 493, 1 (2010) http://dx.doi.org/10.1016/j.physrep.2010.04.001[Crossref]
• [16] S. Tsujikawa, arXiv:1004.1493 [astro-ph.CO]
• [17] L. Amendola, S. Tsujikawa, Dark Energy (Cambridge University press, 2010)
• [18] M. Li, X. D. Li, S. Wang, Y. Wang, Commun. Theor. Phys. 56, 525 (2011) http://dx.doi.org/10.1088/0253-6102/56/3/24[Crossref]
• [19] K. Bamba, S. Capozziello, S. Nojiri, S. D. Odintsov, Astrophys. Space Sci. 342, 155 (2012) http://dx.doi.org/10.1007/s10509-012-1181-8[Crossref]
• [20] S. Nojiri, S. D. Odintsov, Phys. Rept. 505, 59 (2011) http://dx.doi.org/10.1016/j.physrep.2011.04.001[Crossref]
• [21] S. Nojiri, S. D. Odintsov, eConf C0602061, 06 (2006) [Int. J. Geom. Meth. Mod. Phys. 4, 115 (2007)]
• [22] T. P. Sotiriou, V. Faraoni, Rev. Mod. Phys. 82, 451 (2010) http://dx.doi.org/10.1103/RevModPhys.82.451[Crossref]
• [23] S. Capozziello, V. Faraoni, Beyond Einstein Gravity (Springer, 2010)
• [24] S. Capozziello, M. De Laurentis, Phys. Rept. 509, 167 (2011) http://dx.doi.org/10.1016/j.physrep.2011.09.003[Crossref]
• [25] A. De Felice, S. Tsujikawa, Living Rev. Rel. 13, 3 (2010)
• [26] T. Clifton, P. G. Ferreira, A. Padilla, C. Skordis, Phys. Rept. 513, 1 (2012) http://dx.doi.org/10.1016/j.physrep.2012.01.001[Crossref]
• [27] S. Capozziello, M. De Laurentis, S. D. Odintsov, arXiv:1206.4842[gr-qc]
• [28] R. R. Caldwell, M. Kamionkowski, N. N. Weinberg, Phys. Rev. Lett. 91, 071301 (2003) http://dx.doi.org/10.1103/PhysRevLett.91.071301[Crossref]
• [29] B. McInnes, J. High. Energy Phys. 0208, 029 (2002) http://dx.doi.org/10.1088/1126-6708/2002/08/029[Crossref]
• [30] S. Nojiri, S. D. Odintsov, Phys. Lett. B 562, 147 (2003) http://dx.doi.org/10.1016/S0370-2693(03)00594-X[Crossref]
• [31] S. Nojiri, S. D. Odintsov, Phys. Lett. B 571, 1 (2003) http://dx.doi.org/10.1016/j.physletb.2003.08.013[Crossref]
• [32] V. Faraoni, Int. J. Mod. Phys. D 11, 471 (2002) http://dx.doi.org/10.1142/S0218271802001809[Crossref]
• [33] P. F. Gonzalez-Diaz, Phys. Lett. B 586, 1 (2004) http://dx.doi.org/10.1016/j.physletb.2003.12.077[Crossref]
• [34] E. Elizalde, S. Nojiri, S. D. Odintsov, Phys. Rev. D 70, 043539 (2004) http://dx.doi.org/10.1103/PhysRevD.70.043539[Crossref]
• [35] P. Singh, M. Sami, N. Dadhich, Phys. Rev. D 68, 023522 (2003) http://dx.doi.org/10.1103/PhysRevD.68.023522[Crossref]
• [36] C. Csaki, N. Kaloper, J. Terning, Annals Phys. 317, 410 (2005) http://dx.doi.org/10.1016/j.aop.2004.11.015[Crossref]
• [37] P. X. Wu, H. W. Yu, Nucl. Phys. B 727, 355 (2005) http://dx.doi.org/10.1016/j.nuclphysb.2005.07.022[Crossref]
• [38] S. Nesseris, L. Perivolaropoulos, Phys. Rev. D 70, 123529 (2004) http://dx.doi.org/10.1103/PhysRevD.70.123529[Crossref]
• [39] M. Sami, A. Toporensky, Mod. Phys. Lett. A 19, 1509 (2004) http://dx.doi.org/10.1142/S0217732304013921[Crossref]
• [40] H. Stefancic, Phys. Lett. B 586, 5 (2004) http://dx.doi.org/10.1016/j.physletb.2004.02.018[Crossref]
• [41] L. P. Chimento, R. Lazkoz, Phys. Rev. Lett. 91, 211301 (2003) http://dx.doi.org/10.1103/PhysRevLett.91.211301[Crossref]
• [42] J. G. Hao, X. Z. Li, Phys. Lett. B 606, 7 (2005) http://dx.doi.org/10.1016/j.physletb.2004.11.079[Crossref]
• [43] E. Elizalde, S. Nojiri, S. D. Odintsov, P. Wang, Phys. Rev. D 71, 103504 (2005) http://dx.doi.org/10.1103/PhysRevD.71.103504[Crossref]
• [44] M. P. Dabrowski, T. Stachowiak, Annals Phys. 321, 771 (2006) http://dx.doi.org/10.1016/j.aop.2005.10.006[Crossref]
• [45] F. S. N. Lobo, Phys. Rev. D 71, 084011 (2005) http://dx.doi.org/10.1103/PhysRevD.71.084011[Crossref]
• [46] R. G. Cai, H. S. Zhang, A. Wang, Commun. Theor. Phys. 44, 948 (2005) http://dx.doi.org/10.1088/6102/44/5/948[Crossref]
• [47] I. Y. Aref’eva, A. S. Koshelev, S. Y. Vernov, Phys. Rev. D 72, 064017 (2005) http://dx.doi.org/10.1103/PhysRevD.72.064017[Crossref]
• [48] H. Q. Lu, Z. G. Huang, W. Fang, arXiv:hepth/0504038
• [49] W. Godlowski, M. Szydlowski, Phys. Lett. B 623, 10 (2005) http://dx.doi.org/10.1016/j.physletb.2005.07.044[Crossref]
• [50] J. Sola, H. Stefancic, Phys. Lett. B 624, 147 (2005) http://dx.doi.org/10.1016/j.physletb.2005.08.051[Crossref]
• [51] B. Guberina, R. Horvat, H. Nikolic, Phys. Rev. D 72, 125011 (2005) http://dx.doi.org/10.1103/PhysRevD.72.125011[Crossref]
• [52] Y. Shtanov, V. Sahni, Class. Quant. Grav. 19, L101 (2002) http://dx.doi.org/10.1088/0264-9381/19/11/102[Crossref]
• [53] J. D. Barrow, Class. Quant. Grav. 21, L79 (2004) http://dx.doi.org/10.1088/0264-9381/21/11/L03[Crossref]
• [54] S. Nojiri, S. D. Odintsov, Phys. Lett. B 595, 1 (2004) http://dx.doi.org/10.1016/j.physletb.2004.06.060[Crossref]
• [55] S. Nojiri, S. D. Odintsov, Phys. Rev. D 70, 103522 (2004) http://dx.doi.org/10.1103/PhysRevD.70.103522[Crossref]
• [56] S. Nojiri, S. D. Odintsov, Phys. Rev. D 72, 023003 (2005) http://dx.doi.org/10.1103/PhysRevD.72.023003[Crossref]
• [57] S. Cotsakis, I. Klaoudatou, J. Geom. Phys. 55, 306 (2005) http://dx.doi.org/10.1016/j.geomphys.2004.12.012[Crossref]
• [58] M. P. Dabrowski, Phys. Rev. D 71, 103505 (2005) http://dx.doi.org/10.1103/PhysRevD.71.103505[Crossref]
• [59] L. Fernandez-Jambrina, R. Lazkoz, Phys. Rev. D 70, 121503 (2004) http://dx.doi.org/10.1103/PhysRevD.70.121503[Crossref]
• [60] L. Fernandez-Jambrina, R. Lazkoz, Phys. Lett. B 670, 254 (2009) http://dx.doi.org/10.1016/j.physletb.2008.10.061[Crossref]
• [61] J. D. Barrow, C. G. Tsagas, Class. Quant. Grav. 22, 1563 (2005) http://dx.doi.org/10.1088/0264-9381/22/9/006[Crossref]
• [62] H. Stefancic, Phys. Rev. D 71, 084024 (2005) http://dx.doi.org/10.1103/PhysRevD.71.084024[Crossref]
• [63] C. Cattoen, M. Visser, Class. Quant. Grav. 22, 4913 (2005) http://dx.doi.org/10.1088/0264-9381/22/23/001[Crossref]
• [64] P. Tretyakov, A. Toporensky, Y. Shtanov, V. Sahni, Class. Quant. Grav. 23, 3259 (2006) http://dx.doi.org/10.1088/0264-9381/23/10/001[Crossref]
• [65] A. Balcerzak, M. P. Dabrowski, Phys. Rev. D 73, 101301 (2006) http://dx.doi.org/10.1103/PhysRevD.73.101301[Crossref]
• [66] M. Sami, P. Singh, S. Tsujikawa, Phys. Rev. D 74, 043514 (2006) http://dx.doi.org/10.1103/PhysRevD.74.043514[Crossref]
• [67] M. Bouhmadi-Lopez, P. F. Gonzalez-Diaz, P. Martin-Moruno, Phys. Lett. B 659, 1 (2008) http://dx.doi.org/10.1016/j.physletb.2007.10.079[Crossref]
• [68] A. V. Yurov, A. V. Astashenok, P. F. Gonzalez-Diaz, Grav. Cosmol. 14, 205 (2008) http://dx.doi.org/10.1134/S0202289308030018[Crossref]
• [69] T. Koivisto, Phys. Rev. D 77, 123513 (2008) http://dx.doi.org/10.1103/PhysRevD.77.123513[Crossref]
• [70] J. D. Barrow, S. Z. W. Lip, Phys. Rev. D 80, 043518 (2009) http://dx.doi.org/10.1103/PhysRevD.80.043518[Crossref]
• [71] M. Bouhmadi-Lopez, Y. Tavakoli, P. V. Moniz, J. Cosmol. Aatropart. P. 1004, 016 (2010) http://dx.doi.org/10.1088/1475-7516/2010/04/016[Crossref]
• [72] S. Nojiri, S. D. Odintsov, S. Tsujikawa, Phys. Rev. D 71, 063004 (2005) http://dx.doi.org/10.1103/PhysRevD.71.063004[Crossref]
• [73] S. Nojiri, S. D. Odintsov, Phys. Rev. D 78, 046006 (2008) http://dx.doi.org/10.1103/PhysRevD.78.046006[Crossref]
• [74] K. Bamba, S. Nojiri, S. D. Odintsov, J. Cosmol. Aatropart. P. 0810, 045 (2008) http://dx.doi.org/10.1088/1475-7516/2008/10/045[Crossref]
• [75] K. Bamba, S. D. Odintsov, L. Sebastiani, S. Zerbini, Eur. Phys. J. C 67 (2010) 295 http://dx.doi.org/10.1140/epjc/s10052-010-1292-8[Crossref]
• [76] P. J. Steinhardt, N. Turok, Phys. Rev. D 65, 126003 (2002) http://dx.doi.org/10.1103/PhysRevD.65.126003[Crossref]
• [77] P. J. Steinhardt, N. Turok, arXiv:hep-th/0111030
• [78] J. Khoury, B. A. Ovrut, P. J. Steinhardt, N. Turok, Phys. Rev. D 66, 046005 (2002) http://dx.doi.org/10.1103/PhysRevD.66.046005[Crossref]
• [79] P. J. Steinhardt, N. Turok, Nucl. Phys. Proc. Suppl. 124, 38 (2003) http://dx.doi.org/10.1016/S0920-5632(03)02075-9[Crossref]
• [80] P. J. Steinhardt, N. Turok, Science 296, 1436 (2002) http://dx.doi.org/10.1126/science.1070462[Crossref]
• [81] J. Khoury, P. J. Steinhardt, N. Turok, Phys. Rev. Lett. 92, 031302 (2004) http://dx.doi.org/10.1103/PhysRevLett.92.031302[Crossref]
• [82] P. J. Steinhardt, N. Turok, Science 312, 1180 (2006) http://dx.doi.org/10.1126/science.1126231[Crossref]
• [83] D. Y. Chung, arXiv:physics/0105064
• [84] K. Saaidi, H. Sheikhahmadi, A. H. Mohammadi, Astrophys. Space Sci. 338, 355 (2012) http://dx.doi.org/10.1007/s10509-011-0944-y[Crossref]
• [85] S. Nojiri, S. D. Odintsov, D. Saez-Gomez, AIP Conf. Proc. 1458, 207 (2011)
• [86] Y. F. Cai, E. N. Saridakis, J. Cosmol. 17, 7238 (2011)
• [87] T. Biswas, A. Mazumdar, Phys. Rev. D 80, 023519 (2009) http://dx.doi.org/10.1103/PhysRevD.80.023519[Crossref]
• [88] T. Biswas, T. Koivisto, A. Mazumdar, J. Cosmol. Aatropart. P. 1011, 008 (2010) http://dx.doi.org/10.1088/1475-7516/2010/11/008[Crossref]
• [89] T. Biswas, E. Gerwick, T. Koivisto, A. Mazumdar, Phys. Rev. Lett. 108, 031101 (2012) http://dx.doi.org/10.1103/PhysRevLett.108.031101[Crossref]
• [90] V. Sahni, A. Toporensky, Phys. Rev. D 85, 123542 (2012) http://dx.doi.org/10.1103/PhysRevD.85.123542[Crossref]
• [91] J. Khoury, B. A. Ovrut, P. J. Steinhardt, N. Turok, Phys. Rev. D 64, 123522 (2001) http://dx.doi.org/10.1103/PhysRevD.64.123522[Crossref]
• [92] J. Khoury, B. A. Ovrut, P. J. Steinhardt, N. Turok, arXiv:hep-th/0105212
• [93] R. Y. Donagi, J. Khoury, B. A. Ovrut, P. J. Steinhardt, N. Turok, J. High. Energy Phys. 0111, 041 (2001) http://dx.doi.org/10.1088/1126-6708/2001/11/041[Crossref]
• [94] J. Khoury, B. A. Ovrut, P. J. Steinhardt, N. Turok, Phys. Rev. D 66, 046005 (2002) http://dx.doi.org/10.1103/PhysRevD.66.046005[Crossref]
• [95] D. N. Page, Class. Quant. Grav. 1, 417 (1984) http://dx.doi.org/10.1088/0264-9381/1/4/015[Crossref]
• [96] P. Peter, N. Pinto-Neto, Phys. Rev. D 65, 023513 (2001) http://dx.doi.org/10.1103/PhysRevD.65.023513[Crossref]
• [97] P. Peter, N. Pinto-Neto, Phys. Rev. D 66, 063509 (2002) http://dx.doi.org/10.1103/PhysRevD.66.063509[Crossref]
• [98] Y. Shtanov, V. Sahni, Phys. Lett. B 557, 1 (2003) http://dx.doi.org/10.1016/S0370-2693(03)00179-5[Crossref]
• [99] T. Biswas, A. Mazumdar, W. Siegel, J. Cosmol. Aatropart. P. 0603, 009 (2006) http://dx.doi.org/10.1088/1475-7516/2006/03/009[Crossref]
• [100] Y. F. Cai, T. Qiu, Y. S. Piao, M. Li, X. Zhang, J. High. Energy Phys. 0710, 071 (2007) http://dx.doi.org/10.1088/1126-6708/2007/10/071[Crossref]
• [101] P. Creminelli, L. Senatore, J. Cosmol. Aatropart. P. 0711, 010 (2007) http://dx.doi.org/10.1088/1475-7516/2007/11/010[Crossref]
• [102] Y. S. Piao, Phys. Lett. B 677, 1 (2009) http://dx.doi.org/10.1016/j.physletb.2009.05.009[Crossref]
• [103] J. Zhang, Z. G. Liu, Y. S. Piao, Phys. Rev. D 82, 123505 (2010) http://dx.doi.org/10.1103/PhysRevD.82.123505[Crossref]
• [104] Y. S. Piao, Phys. Lett. B 691, 225 (2010) http://dx.doi.org/10.1016/j.physletb.2010.06.039[Crossref]
• [105] Z. -G. Liu, Y. -S. Piao, Phys. Rev. D 86, 083510 (2012) http://dx.doi.org/10.1103/PhysRevD.86.083510[Crossref]
• [106] P. P. Avelino, R. Z. Ferreira, Phys. Rev. D 86, 041501 (2012) http://dx.doi.org/10.1103/PhysRevD.86.041501[Crossref]
• [107] C. Corda, H. J. Mosquera Cuesta, Astropart. Phys. 34, 587 (2011) http://dx.doi.org/10.1016/j.astropartphys.2010.12.002[Crossref]
• [108] M. Novello, S. E. P. Bergliaffa, Phys. Rept. 463, 127 (2008) http://dx.doi.org/10.1016/j.physrep.2008.04.006[Crossref]
• [109] R. Myrzakulov, Gen. Rel. Grav. 44, 3059 (2012) http://dx.doi.org/10.1007/s10714-012-1439-z[Crossref]
• [110] R. Myrzakulov arXiv:1204.1093 [physics.gen-ph]
• [111] R. Myrzakulov et al., Int. J. Theor. Phys. 51, 1204 (2012) http://dx.doi.org/10.1007/s10773-011-0996-3[Crossref]
• [112] M. Jamil, N. A. Myrzakulov, K. K. Yerzhanov, D. Momeni, R. Myrzakulov, arXiv:1201.4360 [physics.genph]
• [113] H. Itoyama, A. Mironov, A. Morozov and A. Morozov, J. High. Energy Phys. 1207, 131 (2012) [arXiv:1203.5978 [hep-th]]. http://dx.doi.org/10.1007/JHEP07(2012)131[Crossref]
• [114] G. W. Gibbons, M. Vyska, Class. Quant. Grav. 29, 065016 (2012) http://dx.doi.org/10.1088/0264-9381/29/6/065016[Crossref]
• [115] I. Bochicchio, S. Capozziello, E. Laserra, Int. J. Geom. Meth. Mod. Phys. 8, 1653 (2011) http://dx.doi.org/10.1142/S0219887811005865[Crossref]
• [116] B. G. Dimitrov, J. Math. Phys. 44, 2542 (2003) http://dx.doi.org/10.1063/1.1560855[Crossref]
• [117] J. D’Ambroise, arXiv:0908.2481 [gr-qc]
• [118] R. Teh, P. -Y. Tan, K. -M. Wong, Int. J. Mod. Phys. A 27, 1250148 (2012) http://dx.doi.org/10.1142/S0217751X12501485[Crossref]
• [119] V. P. Spiridonov, G. S. Vartanov, J. High. Energy Phys. 1206, 016 (2012) http://dx.doi.org/10.1007/JHEP06(2012)016[Crossref]
• [120] M. Jamil, N. A. Myrzakulov, K. K. Yerzhanov, D. Momeni, R. Myrzakulov, arXiv:1201.4360[physics.genph]
• [121] A. J. Lopez-Revelles, R. Myrzakulov, D. Saez-Gomez, Phys. Rev. D 85, 103521 (2012) http://dx.doi.org/10.1103/PhysRevD.85.103521[Crossref]
• [122] M. Sharif, K. R. Yesmakhanova, S. Rani, R. Myrzakulov, arXiv:1204.2181 [physics.gen-ph]
• [123] R. Myrzakulov, arXiv:1205.5266 [physics.gen-ph]
• [124] K. Bamba, O. Razina, K. Yerzhanov, R. Myrzakulov, arXiv:1203.2804 [physics.gen-ph]
• [125] T. Chiba, T. Okabe, M. Yamaguchi, Phys. Rev. D 62, 023511 (2000) http://dx.doi.org/10.1103/PhysRevD.62.023511[Crossref]
• [126] C. Armendariz-Picon, T. Damour, V. F. Mukhanov, Phys. Lett. B 458, 209 (1999) http://dx.doi.org/10.1016/S0370-2693(99)00603-6[Crossref]
• [127] J. Garriga, V. F. Mukhanov, Phys. Lett. B 458, 219 (1999) http://dx.doi.org/10.1016/S0370-2693(99)00602-4[Crossref]
• [128] C. Armendariz-Picon, V. F. Mukhanov, P. J. Steinhardt, Phys. Rev. Lett. 85, 4438 (2000) http://dx.doi.org/10.1103/PhysRevLett.85.4438[Crossref]
• [129] C. Armendariz-Picon, V. F. Mukhanov, P. J. Steinhardt, Phys. Rev. D 63, 103510 (2001) http://dx.doi.org/10.1103/PhysRevD.63.103510[Crossref]
• [130] R. de Putter, E. V. Linder, Astropart. Phys. 28, 263 (2007) http://dx.doi.org/10.1016/j.astropartphys.2007.05.011[Crossref]
• [131] R. Myrzakulov, arXiv:1011.4337 [astro-ph.CO]
• [132] T. Damour, C. Hillmann, J. High. Energy Phys. 0908, 100 (2009) http://dx.doi.org/10.1088/1126-6708/2009/08/100[Crossref]
• [133] T. Damour, P. Spindel, Phys. Rev. D 83, 123520 (2011) http://dx.doi.org/10.1103/PhysRevD.83.123520[Crossref]
• [134] A. Y. Kamenshchik, U. Moschella, V. Pasquier, Phys. Lett. B 511, 265 (2001) http://dx.doi.org/10.1016/S0370-2693(01)00571-8[Crossref]
• [135] M. C. Bento, O. Bertolami, A. A. Sen, Phys. Rev. D 66, 043507 (2002) http://dx.doi.org/10.1103/PhysRevD.66.043507[Crossref]
• [136] K. Bamba, U. Debnath, K. Yesmakhanova, P. Tsyba, G. Nugmanova, R. Myrzakulov, Entropy 14, 2351 (2012) http://dx.doi.org/10.3390/e14112351[Crossref]
• [137] S. Nojiri, S. D. Odintsov, Phys. Rev. D 72, 023003 (2005) http://dx.doi.org/10.1103/PhysRevD.72.023003[Crossref]
• [138] H. Stefancic, Phys. Rev. D 71, 084024 (2005) http://dx.doi.org/10.1103/PhysRevD.71.084024[Crossref]
• [139] U. Alam, V. Sahni, T. D. Saini, A. A. Starobinsky, Mon. Not. Roy. Astron. Soc. 354, 275 (2004) http://dx.doi.org/10.1111/j.1365-2966.2004.08189.x[Crossref]
• [140] U. Alam, V. Sahni, A. A. Starobinsky, J. Cosmol. Aatropart. P. 0406, 008 (2004) http://dx.doi.org/10.1088/1475-7516/2004/06/008[Crossref]
• [141] U. Alam, V. Sahni, A. A. Starobinsky, J. Cosmol. Aatropart. P. 0702, 011 (2007) http://dx.doi.org/10.1088/1475-7516/2007/02/011[Crossref]
• [142] S. Nesseris, L. Perivolaropoulos, J. Cosmol. Aatropart. P. 0701, 018 (2007) http://dx.doi.org/10.1088/1475-7516/2007/01/018[Crossref]
• [143] P. U. Wu, H. W. Yu, Phys. Lett. B 643, 315 (2006) http://dx.doi.org/10.1016/j.physletb.2006.11.021[Crossref]
• [144] H. K. Jassal, J. S. Bagla, T. Padmanabhan, Mon. Not. Roy. Astron. Soc. 405, 2639 (2010)
• [145] Edited by M. Abramowitz, l. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (1964)
• [146] A. A. Starobinsky, JETP Lett. 68, 757 (1998) [Pisma Zh. Eksp. Teor. Fiz. 68, 721 (1998)] http://dx.doi.org/10.1134/1.567941[Crossref]
• [147] D. Huterer, M. S. Turner, Phys. Rev. D 60, 081301 (1999) http://dx.doi.org/10.1103/PhysRevD.60.081301[Crossref]
• [148] T. Nakamura, T. Chiba, Mon. Not. Roy. Astron. Soc. 306, 696 (1999) http://dx.doi.org/10.1046/j.1365-8711.1999.02551.x[Crossref]
• [149] V. Sahni, A. Starobinsky, Int. J. Mod. Phys. D 15, 2105 (2006) http://dx.doi.org/10.1142/S0218271806009704[Crossref]
• [150] A. A. Starobinsky, Grav. Cosmol. 6, 157 (2000)
• [151] A. A. Starobinsky, Sov. Astron. Lett. 4, 82 (1978)
• [152] B. Feng, M. Li, Y. S. Piao, X. Zhang, Phys. Lett. B 634, 101 (2006) http://dx.doi.org/10.1016/j.physletb.2006.01.066[Crossref]
• [153] E. Elizalde, S. Nojiri, S. D. Odintsov, Phys. Rev. D 70, 043539 (2004) http://dx.doi.org/10.1103/PhysRevD.70.043539[Crossref]
• [154] B. Feng, X. L. Wang, X. M. Zhang, Phys. Lett. B 607, 35 (2005) http://dx.doi.org/10.1016/j.physletb.2004.12.071[Crossref]
• [155] X. F. Zhang, H. Li, Y. S. Piao, X. M. Zhang, Mod. Phys. Lett. A 21, 231 (2006) http://dx.doi.org/10.1142/S0217732306018469[Crossref]
• [156] M. z. Li, B. Feng, X. m. Zhang, J. Cosmol. Aatropart. P. 0512, 002 (2005) http://dx.doi.org/10.1088/1475-7516/2005/12/002[Crossref]
• [157] G. B. Zhao, J. Q. Xia, M. Li, B. Feng, X. Zhang, Phys. Rev. D 72, 123515 (2005) http://dx.doi.org/10.1103/PhysRevD.72.123515[Crossref]
• [158] C. Corda, Int. J. Mod. Phys. D 18, 2275 (2009) http://dx.doi.org/10.1142/S0218271809015904[Crossref]

Identifiers

DOI

10.2478/s11534-013-0187-3