Abstract
In this study, we have constructed a viable cosmological model characterized by the presence of the Gauss–Bonnet four-dimensional invariant, higher-order corrections to the low energy effective action motivated from heterotic superstring theory and a general exponential potential comparable to those obtained in higher dimensional supergravities. The field equations were studied by assuming a particular relation between the Hubble parameter and the time derivative of the scalar field. It was observed that, for specific relations between the free parameters in the theory, the universe is cyclic, expands and contracts alternately without singularity with an equation of state oscillating around −1. The model is found to fit the recent astrophysical data.
Acknowledgment
I would like to thank the anonymous referee for his useful comments and valuable suggestions.
Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: The author received no direct funding for this work.
Conflict of interest statement: The author declares that he has no conflicts of interest.
References
[1] A. G. Riess, A. V. Filippenko, P. Challis, et al.., “Observational evidence from supernovae for an accelerating Universe and a cosmological constant,” Astron. J., vol. 116, p. 1009, 1998. https://doi.org/10.1086/300499.Search in Google Scholar
[2] S. Perlmutter, G. Aldering, G. Goldhaber, et al.., “Measurements of omega and lambda from 42 high-redshift supernovae,” Astrophys. J., vol. 517, p. 565, 1999. https://doi.org/10.1086/307221.Search in Google Scholar
[3] K. Abazajian, J. K. Adelman-McCarthy, M. A. Agüeros, et al.., “The third data release of the sloan digital sky survey,” Astron. J., vol. 129, p. 1755, 2005.10.1086/427544Search in Google Scholar
[4] D. N. Spergel, L. Verde, H. V. Peiris, et al.., “First year Wilkinson microwave anisotropy probe (WMAP) observations: determination of cosmological parameters,” Astrophys. J. Suppl., vol. 148, p. 175, 2003. https://doi.org/10.1086/377226.Search in Google Scholar
[5] E. Komatsu, J. Dunkley, M. R. Nolta, et al.., “Five-year Wilkinson microwave anisotropy probe (WMAP) observations: cosmological interpretation,” Astrophys. J. Suppl., vol. 180, p. 330, 2009. https://doi.org/10.1088/0067-0049/180/2/330.Search in Google Scholar
[6] K. Abazajian, J. K. Adelman-McCarthy, M. A. Agüeros, et al.., “The second data release of the sloan digital sky survey,” Astron. J., vol. 128, p. 502, 2004.10.1086/421365Search in Google Scholar
[7] S. Masi, P. A. R. Ade, J. J. Bock, et al.., “The BOOMRanG experiment and the curvature of the universe,” Prog. Part. Nucl. Phys., vol. 48, pp. 243–261, 2002. https://doi.org/10.1016/s0146-6410(02)00131-x.Search in Google Scholar
[8] A. H. Jaffe, P. A. R. Ade, A. Balbi, et al.., “Cosmology from maxima-1, boomrang and COBE/DMR CMB observations,” Phys. Rev. Lett., vol. 86, pp. 3475–3479, 2001. https://doi.org/10.1103/physrevlett.86.3475.Search in Google Scholar
[9] A. D. Linde, Particle Physics and Inflationary Cosmology, Chur, Switzerland, Hardwood Academic, 1990.10.1201/9780367807788Search in Google Scholar
[10] A. R. Liddle and D. H. Lyth, Cosmological Inflation and Large-Scale Structure, Cambridge, UK, Cambridge University Press, 2000.10.1017/CBO9781139175180Search in Google Scholar
[11] I. Zlatev, L. Wang, and P. J. Steinhardt, “Quintessence, cosmic coincidence, and the cosmological constant,” Phys. Rev. Lett., vol. 82, p. 896, 1999. https://doi.org/10.1103/physrevlett.82.896.Search in Google Scholar
[12] R. R. Caldwell, M. Kamionkowski, and N. N. Weinberg, “Phantom energy: dark energy with w < −1 a cosmic doomsday,” Phys. Rev. Lett., vol. 91, 2003, Art no. 071301. https://doi.org/10.1103/physrevlett.91.071301.Search in Google Scholar
[13] A. Sen, “Tachyon matter,” J. High Energy Phys., vol. 7, 2002, Art no. 65.10.1088/1126-6708/2002/07/065Search in Google Scholar
[14] A. Sen, “Field theory of tachyon matter,” Mod. Phys. Lett., vol. A17, p. 1797, 2002. https://doi.org/10.1142/s0217732302008071.Search in Google Scholar
[15] A. Kamenshchik, U. Moschella, and V. Pasquier, “An alternative to quintessence,” Phys. Lett. B, vol. 511, pp. 265–268, 2001. https://doi.org/10.1016/s0370-2693(01)00571-8.Search in Google Scholar
[16] Y.-F. Cai, E. N. Saridakis, M. R. Setare, and J.-Q. Xia, “Quintom cosmology: theoretical implications and observations,” Phys. Rep., vol. 493, p. 1, 2010. https://doi.org/10.1016/j.physrep.2010.04.001.Search in Google Scholar
[17] P. Horava and D. Minic, “Probable values of the cosmological constant in a holographic theory,” Phys. Rev. Lett., vol. 85, pp. 1610–1613, 2000. https://doi.org/10.1103/PhysRevLett.85.1610.Search in Google Scholar
[18] S. Roy, S. Chattopadhyay, and A. Pasqua, “A study on the dependence of the dimensionless Brans–Dicke parameter on the scalar field and their time dependence,” Eur. Phys. J. Plus, vol. 128, pp. 1–16, 2013. https://doi.org/10.1140/epjp/i2013-13147-4.Search in Google Scholar
[19] S. Roy, D. Laha, A. A. Sangma, and I. Pal, “A study on the expanding universe based on a model of the time variation of its matter content in the framework of Brans–Dicke theory,” Int. J. Curr. Res., vol. 8, pp. 32251–32259, 2016.Search in Google Scholar
[20] T. P. Sotiriou and V. Faraoni, “f(R) theories of gravity,” Rev. Mod. Phys., vol. 82, pp. 451–497, 2010. https://doi.org/10.1103/revmodphys.82.451.Search in Google Scholar
[21] R. Ferraro and F. Fiorini, “Modified teleparallel gravity: inflation without an inflaton,” Phys. Rev. D, vol. 75, p. 084031, 2007. https://doi.org/10.1103/physrevd.75.084031.Search in Google Scholar
[22] M. Zubair, M. Zeeshan, and S. Waheed, “Cosmic evolution in the background of R(1 + αQ) gravity,” Mod. Phys. Lett. A, vol. 34, p. 1950253, 2019. https://doi.org/10.1142/s0217732319502535.Search in Google Scholar
[23] M. Sharif and M. Zubair, “Thermodynamics in f(R, T) theory of gravity,” J. Cosmol. Astropart. Phys., vol. 3, p. 28, 2012.10.1088/1475-7516/2012/03/028Search in Google Scholar
[24] S. Deser and R. P. Woodard, “Nonlocal cosmology,” Phys. Rev. Lett., vol. 99, p. 111301, 2007. https://doi.org/10.1103/physrevlett.99.111301.Search in Google Scholar
[25] C. Deffayet and R. P. Woodard, “Reconstructing the distortion function for nonlocal cosmology,” J. Cosmol. Astropart. Phys., vol. 0908, p. 023, 2009. https://doi.org/10.1088/1475-7516/2009/08/023.Search in Google Scholar
[26] U. Debnath, S. Chattopadhyay, and M. Jamil, “Fractional action cosmology: some dark energy models in emergent, logamediate and intermediate scenarios of the universe,” J. Theor. Appl. Phys., vol. 7, p. 25, 2013. https://doi.org/10.1186/2251-7235-7-25.Search in Google Scholar
[27] V. S. Shchigolev, “Testing fractional action cosmology,” Eur. Phys. J. Plus, vol. 131, p. 256, 2016. https://doi.org/10.1140/epjp/i2016-16256-6.Search in Google Scholar
[28] S. Chattopadhyay and A. Pasqua, “Reconstruction of modified holographic Ricci dark energy in El-Nabulsi fractional action cosmology,” Int. J. Theor. Phys., vol. 7, p. 22, 2013. https://doi.org/10.1186/2251-7235-7-22.Search in Google Scholar
[29] R. A. El-Nabulsi, “Gravitons in fractional action cosmology,” Int. J. Theor. Phys., vol. 51, p. 3978, 2012. https://doi.org/10.1007/s10773-012-1290-8.Search in Google Scholar
[30] R. A. El-Nabulsi, “Fractional derivatives generalization of Einstein’s field equations,” Indian J. Phys., vol. 87, pp. 195–200, 2013. https://doi.org/10.1007/s12648-012-0201-4.Search in Google Scholar
[31] R. A. El-Nabulsi, “Oscillating flat FRW dark energy dominated cosmology from periodic functional approach,” Commun. Theor. Phys., vol. 54, p. 16, 2010.10.1088/0253-6102/54/1/03Search in Google Scholar
[32] R. A. El-Nabulsi, “Fractional action oscillating phantom cosmology with conformal coupling,” Eur. Phys. J. Plus, vol. 103, p. 102, 2015.Search in Google Scholar
[33] R. A. El-Nabulsi, “A modified gravity theory with time-dependent exponent,” Eur. Phys. J. Plus, vol. 126, p. 114, 2011. https://doi.org/10.1140/epjp/i2011-11114-9.Search in Google Scholar
[34] S. Nojiri, S. D. Odintsov, and V. K. Oikonomou, “Modified gravity theories on a nutshell: inflation, bounce and late-time evolution,” Phys. Rep., vol. 692, pp. 1–104, 2017. https://doi.org/10.1016/j.physrep.2017.06.001.Search in Google Scholar
[35] S. Nojiri and S. D. Odintsov, “Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models,” Phys. Rep., vol. 505, pp. 59–144, 2011. https://doi.org/10.1016/j.physrep.2011.04.001.Search in Google Scholar
[36] S. Nojiri and S. D. Odintsov, “Introduction to modified gravity and gravitational alternative for dark energy,” Int. J. Geomet. Methods Mod. Phys., vol. 4, pp. 115–146, 2007. https://doi.org/10.1142/s0219887807001928.Search in Google Scholar
[37] R. A. El-Nabulsi, “Dark energy in five-dimensional Brans–Dicke cosmology with dimensional reduction,” Res. Astron. Astrophys., vol. 7, p. 759, 2011. https://doi.org/10.1088/1674-4527/11/7/002.Search in Google Scholar
[38] L.-e. Qiang, Y. Ma, M. Han, and D. Yu, “5-dimensional Brans–Dicke theory and cosmic acceleration,” Phys. Rev. D, vol. 71, p. 061501, 2005. https://doi.org/10.1103/physrevd.71.061501.Search in Google Scholar
[39] R. A. El-Nabulsi, “Living with phantoms fields in a sheet space–time,” Gen. Relat. Gravit., vol. 42, p. 1381, 2010. https://doi.org/10.1007/s10714-009-0911-x.Search in Google Scholar
[40] R. A. El-Nabulsi, “Noncommutative accelerated multidimensional universe dominated by quintessence,” Astrophys. Space Sci., vol. 326, p. 163, 2010. https://doi.org/10.1007/s10509-009-0259-4.Search in Google Scholar
[41] R. A. El-Nabulsi, “Effective 3-brane Brans–Dicke cosmology,” Mod. Phys. Lett. A, vol. 6, p. 401, 2008. https://doi.org/10.1142/s0217732308026327.Search in Google Scholar
[42] R. A. El-Nabulsi, “Accelerated d-dimensional compactified universe in Gauss–Bonnet-dilatonic scalar gravity from brane/M-theory,” Chin. Phys. Lett., vol. 25, p. 2785, 2008.10.1088/0256-307X/25/8/014Search in Google Scholar
[43] R. A. El-Nabulsi, “Phase transitions in the early universe with negatively induced supergravity cosmological constant,” Chin. Phys. Lett., vol. 23, p. 1124, 2006.10.1088/0256-307X/23/5/017Search in Google Scholar
[44] R. A. El-Nabulsi, “Modified braneworld cosmologies in the presence of stringy corrections coupled to a canonical scalar field,” Int. J. Mod. Phys., vol. 18, p. 691, 2009. https://doi.org/10.1142/s0218271809014716.Search in Google Scholar
[45] R. A. El-Nabulsi, “Charged Randall–Sundrum braneworld type II with higher order curvature corrections from superstring arguments and dominated by quintessence,” Commun. Theor. Phys., vol. 53, p. 869, 2010.10.1088/0253-6102/53/5/16Search in Google Scholar
[46] R. A. El-Nabulsi, “Scalar tensor cosmology with kinetic, Gauss–Bonnet and nonminimal derivative couplings and supersymmetric loop corrected potential,” Commun. Theor. Phys., vol. 71, pp. 831–832, 2019. https://doi.org/10.1088/0253-6102/71/7/831.Search in Google Scholar
[47] R. A. El-Nabulsi, “Conformal cosmology with a complex scalar field and a gauge-mediated supersymmetry breaking potential,” Z. Naturforsch., vol. 73, pp. 363–369, 2018. https://doi.org/10.1515/zna-2017-0440.Search in Google Scholar
[48] W.-F. Wang and S.-Z. Yang, “Exact inflationary solution to nonminimally coupled scalar field,” Chin. Phys. Lett., vol. 22, p. 1296, 2005.10.1088/0256-307X/22/5/076Search in Google Scholar
[49] R. A. El-Nabulsi, “Symmetry breaking and conformal coupling with a generalized Higgs potential and the role of the generalized Duffin–Loret equation in the early universe,” Eur. Phys. J. Plus, vol. 129, p. 220, 2014.10.1140/epjp/i2014-14220-2Search in Google Scholar
[50] R. A. El-Nabulsi, “Effective cosmological constant from supergravity arguments and non-minimal coupling,” Phys. Lett. B, vol. 619, pp. 26–29, 2005. https://doi.org/10.1016/j.physletb.2005.06.002.Search in Google Scholar
[51] R. A. El-Nabulsi, “Dark energy from logarithmically modified gravity and deformed Coleman–Weinberg potential,” Res. Astron. Astrophys., vol. 11, p. 759, 2011. https://doi.org/10.1088/1674-4527/11/7/002.Search in Google Scholar
[52] R. A. El-Nabulsi, “Accelerated cosmic expansion from Gauss–Bonnet curvature corrections, nonminimal coupling, and infrared second-order gauge gravity,” Astrophys. Space Sci., vol. 325, pp. 149–152, 2010. https://doi.org/10.1007/s10509-009-0209-1.Search in Google Scholar
[53] M. R. Setare and E. N. Saridakis, “Non-minimally coupled canonical, phantom and quintom models of holographic dark energy,” Phys. Lett. B, vol. 671, pp. 331–338, 2009. https://doi.org/10.1016/j.physletb.2008.12.026.Search in Google Scholar
[54] D. J. Holden and D. Wands, “Self-similar cosmological solutions with a non-minimally coupled scalar field,” Phys. Rev. D, vol. 61, p. 043506, 2000. https://doi.org/10.1103/physrevd.61.043506.Search in Google Scholar
[55] R. A. El-Nabulsi, “Some late-time cosmological aspects of a Gauss–Bonnet gravity with nonminimal coupling a la Brans–Dicke: solutions and perspectives,” Can. J. Phys., vol. 91, pp. 300–321, 2013. https://doi.org/10.1139/cjp-2012-0366.Search in Google Scholar
[56] R. A. El-Nabulsi, “Effective cosmology a la Brans–Dicke with a non-minimally coupling massive inflaton field interacting with minimally coupling massless field,” Braz. J. Phys., vol. 40, pp. 273–282, 2010.Search in Google Scholar
[57] N. Banerjee and K. Ganguly, “Generalised scalar-tensor theory and the cosmic acceleration,” Int. J. Mod. Phys., vol. 18, pp. 445–451, 2009. https://doi.org/10.1142/s0218271809014479.Search in Google Scholar
[58] R. A. El-Nabulsi, “A cosmology governed by a fractional differential equation and the generalized Kilbas–Saigo–Mittag–Leffler function,” Int. J. Theor. Phys., vol. 55, p. 625, 2016. https://doi.org/10.1007/s10773-015-2700-5.Search in Google Scholar
[59] R. A. El-Nabulsi, “Implications of the Ornstein–Uhlenbeck-like fractional differential equation in cosmology,” Rev. Mexic. Fisica, vol. 62, p. 240, 2016.Search in Google Scholar
[60] R. A. El-Nabulsi, “Cosmology with a fractional action principle,” Rom. Rep. Phys., vol. 59, no. 3, p. 763, 2007.Search in Google Scholar
[61] R. A. El-Nabulsi, “Fractional action-like variational approach, perturbed Einstein’s gravity and new cosmology,” Fiz. B, vol. 19, no. 2, p. 103, 2010.Search in Google Scholar
[62] R. A. El-Nabulsi, “Fractional dynamics, fractional weak bosons masses and physics beyond the standard model,” Chaos, Solit. Fractals, vol. 41, pp. 2262–2270, 2009.10.1016/j.chaos.2008.08.033Search in Google Scholar
[63] R. A. El-Nabulsi, “Non-minimal coupling in fractional action cosmology,” Indian J. Phys., vol. 87, p. 835, 2013. https://doi.org/10.1007/s12648-013-0295-3.Search in Google Scholar
[64] R. A. El-Nabulsi, “Fractional action oscillating phantom cosmology with conformal coupling,” Eur. Phys. J. Plus, vol. 130, p. 102, 2015.10.1140/epjp/i2015-15102-9Search in Google Scholar
[65] R. A. El-Nabulsi, “Fractional action cosmology with variable order parameter,” Int. J. Theor. Phys., vol. 56, no. 4, pp. 1159–1182, 2017. https://doi.org/10.1007/s10773-016-3260-z.Search in Google Scholar
[66] R. A. El-Nabulsi, “Accelerated expansion from a modified quadratic gravity,” Astrophys. Space Sci., vol. 332, pp. 491–495, 2010.10.1007/s10509-010-0518-4Search in Google Scholar
[67] R. A. El-Nabulsi, “Dark energy from logarithmic modified gravity and deformed Coleman–Weinberg potential,” Res. Astron. Astrophys., vol. 11, pp. 759–766, 2011. https://doi.org/10.1088/1674-4527/11/7/002.Search in Google Scholar
[68] R. A. El-Nabulsi, “Dark energy in five-dimensional Brans–Dicke cosmology with dimensional reduction,” Res. Astron. Astrophys., vol. 11, pp. 888–894, 2011. https://doi.org/10.1088/1674-4527/11/8/002.Search in Google Scholar
[69] R. A. El-Nabulsi, “Exact solution of a tachyon oscillating cosmology with a supergravity tracking potential,” Eur. Phys. J. Plus, vol. 128, p. 55, 2013. https://doi.org/10.1515/zna-2017-0440.Search in Google Scholar
[70] R. A. El-Nabulsi, “Scalar tensor cosmology with kinetic, Gauss–Bonnet and nonminimal derivative couplings and supersymmetric loop corrected potential,” Commun. Theor. Phys., vol. 17, p. 831, 2019. https://doi.org/10.1088/0253-6102/71/7/831.Search in Google Scholar
[71] R. A. El-Nabulsi, “Non-minimally conformally coupling cosmology with multiple vacua potential with cubic-quintic-septic Duffing oscillator properties,” Z. Naturforsch., vol. 70, pp. 685–694, 2015. https://doi.org/10.1515/zna-2015-0171.Search in Google Scholar
[72] R. A. El-Nabulsi, “Five-dimensional Brans–Dicke compactified universe dominated by a varying speed of light,” Mod. Phys. Lett. A, vol. 35, p. 2050252, 2020. https://doi.org/10.1142/s0217732320502521.Search in Google Scholar
[73] R. A. El-Nabulsi, “Nonstandard Lagrangian cosmology,” J. Theor. Appl. Phys., vol. 7, p. 58, 2013. https://doi.org/10.1186/2251-7235-7-58.Search in Google Scholar
[74] G. Abbas and M. Tahir, “Dynamical instability of non-adiabatic gravitating source in Gauss–Bonnet gravity,” Eur. Phys. J. A, vol. 55, p. 103, 2019. https://doi.org/10.1140/epja/i2019-12776-4.Search in Google Scholar
[75] G. Abbas and M. Tahir, “Models of anisotropic self-gravitating source in Einstein–Gauss–Bonnet gravity,” Adv. High Energy Phys., vol. 2018, 2018, Art no. 7420546. https://doi.org/10.1155/2018/7420546.Search in Google Scholar
[76] N. Banerjee and T. Paul, “Scalar field collapse in Gauss–Bonnet gravity,” Eur. Phys. J. C, vol. 78, p. 130, 2018. https://doi.org/10.1140/epjc/s10052-018-5615-5.Search in Google Scholar
[77] M. Tahir and G. Abbas, “Spherically symmetric gravitational collapse in Einstein Gauss–Bonnet gravity,” Int. J. Geomet. Methods Mod. Phys., vol. 16, p. 1950194, 2014.10.1142/S0219887819501949Search in Google Scholar
[78] M. Tahir and G. Abbas, “Instability of collapsing source under expansion-free condition in Einstein Gauss–Bonnet gravity,” Chin. J. Phys., vol. 61, pp. 8–21, 2019. https://doi.org/10.1016/j.cjph.2019.07.003.Search in Google Scholar
[79] R. A. El-Nabulsi, “Dark energy from “extended modified gravity” and Gauss–Bonnet invariant term,” Astrophys. Space Sci., vol. 327, pp. 161–165, 2010. https://doi.org/10.1007/s10509-010-0330-1.Search in Google Scholar
[80] R. A. El-Nabulsi, “Scalar tensor cosmology with kinetic, Gauss–Bonnet and nonminimal derivative couplings and supersymmetric loop corrected potential,” Commun. Theor. Phys., vol. 71, p. 831, 2019. https://doi.org/10.1088/0253-6102/71/7/831.Search in Google Scholar
[81] R. A. El-Nabulsi, “Accelerated magnetic Gauss–Bonnet cosmology,” Fiz. B, vol. 17, pp. 455–462, 2008.Search in Google Scholar
[82] S. Nojiri and S. D. Odintsov, “Modified f(R) gravity consistent with realistic cosmology: from a matter dominated epoch to a dark energy universe,” Phys. Rev. D, vol. 74, p. 086005, 2006. https://doi.org/10.1103/physrevd.74.086005.Search in Google Scholar
[83] S. Nojiri, S. D. Odintsov, and M. Sami, “Dark energy cosmology from higher-order, string-inspired gravity and its reconstruction,” Phys. Rev. D, vol. 74, p. 046004, 2006. https://doi.org/10.1103/physrevd.74.046004.Search in Google Scholar
[84] L. N. Granda, “Late-time cosmological scenarios from scalar field with Gauss–Bonnet and non-minimal kinetic couplings,” Int. J. Theor. Phys., vol. 51, pp. 2813–2829, 2012. https://doi.org/10.1007/s10773-012-1157-z.Search in Google Scholar
[85] L. N. Granda, “Dark energy from scalar field with Gauss–Bonnet and non-minimal kinetic coupling,” Mod. Phys. Lett. A, vol. 27, p. 1250018, 2012. https://doi.org/10.1142/s0217732312500186.Search in Google Scholar
[86] R. A. El-Nabulsi, “Maxwell brane cosmology with higher-order string curvature corrections, a nonminimally coupled scalar field, dark matter-dark energy interaction and a varying speed of light,” Int. J. Mod. Phys., vol. 18, pp. 289–318, 2009. https://doi.org/10.1142/s0218271809014431.Search in Google Scholar
[87] S. Shahidi, “Cosmology of a higher derivative scalar theory with non-minimal Maxwell coupling,” Eur. Phys. J. C, vol. 79, p. 448, 2019. https://doi.org/10.1140/epjc/s10052-019-6960-8.Search in Google Scholar
[88] R. A. El-Nabulsi, “Dynamical vacuum energy and phantom divide-line cross in scalar cosmology,” Indian J. Phys., vol. 87, pp. 303–307, 2013. https://doi.org/10.1007/s12648-012-0200-5.Search in Google Scholar
[89] A. Tripathi, A. Sangwan, and H. K. Jassal, “Dark energy equation of state parameter and its evolution at low redshift,” J. Cosmol. Astropart. Phys., vol. 06, p. 012, 2017. https://doi.org/10.1088/1475-7516/2017/06/012.Search in Google Scholar
[90] W.-F. Wang, “Exact solution is chaotic inflation model with negative potential,” Chin. Phys. Lett., vol. 20, pp. 593–595, 2004.10.1088/0256-307X/20/4/344Search in Google Scholar
[91] S.-W. Chen, S.-Z. Yang, X.-Z. Hao, and X.-W. Liu, “A kind of exact inflationary solution in the chaotic inflation model to non-minimally coupled scalar field,” Chin. Phys. Lett., vol. 25, pp. 3162–3164, 2008.10.1088/0256-307X/25/9/019Search in Google Scholar
[92] R. A. El-Nabulsi, “Five-dimensional Brans–Dicke M1 × R3 × S1 cosmology with chameleon scalar field,” Astrophys. Space Sci., vol. 327, pp. 111–115, 2010. https://doi.org/10.1007/s10509-010-0281-6.Search in Google Scholar
[93] T. Barreiro, E. J. Copeland, and N. J. Nunes, “Quintessence arising from exponential potentials,” Phys. Rev. D, vol. 61, p. 127301, 2000. https://doi.org/10.1103/physrevd.61.127301.Search in Google Scholar
[94] L. A. Urena-Lopez, “Scalar phantom energy as a cosmological dynamical system,” J. Cosmol. Astropart. Phys., vol. 09, p. 013, 2005. https://doi.org/10.1088/1475-7516/2005/09/013.Search in Google Scholar
[95] I. P. Neupane, “Accelerating cosmologies from exponential potentials,” Class. Quantum Grav., vol. 21, p. 4383, 2004. https://doi.org/10.1088/0264-9381/21/18/007.Search in Google Scholar
[96] A. D. Linde, “Inflation and quantum cosmology,” in Three Hundred Years of Gravitation, S. W. Hawking and W. Israel, Eds., Cambridge, Cambridge University Press, 1987, pp. 604–630.10.1017/CBO9780511564178.016Search in Google Scholar
[97] P. M. Cowdall, H. Lu, C. N. Pope, K. Stelle, and P. K. Townsend, “Domain walls in massive supergravities,” Nucl. Phys. B, vol. 486, pp. 49–76, 1997. https://doi.org/10.1016/s0550-3213(96)00609-8.Search in Google Scholar
[98] S. Pan, E. N. Saridakis, and W. Yang, “Observational constraints on oscillating dark-energy parameterization,” Phys. Rev. D, vol. 98, p. 063510, 2018. https://doi.org/10.1103/physrevd.98.063510.Search in Google Scholar
[99] S. Dodelson, M. Kaplinghat, and E. Stewart, “Solving the coincidence problem: tracking oscillating energy,” Phys. Rev. Lett., vol. 85, p. 5276, 2000. https://doi.org/10.1103/physrevlett.85.5276.Search in Google Scholar
[100] B. Feng, M. Li, Y. S. Piao, and X. Zhang, “Oscillating quintom and the recurrent universe,” Phys. Lett. B, vol. 634, p. 101, 2006. https://doi.org/10.1016/j.physletb.2006.01.066.Search in Google Scholar
[101] S. Kumar, “Observational constraints on Hubble constant and deceleration parameter in power-law cosmology,” Mon. Not. Roy. Astron. Soc., vol. 422, pp. 2532–2538, 2012. https://doi.org/10.1111/j.1365-2966.2012.20810.x.Search in Google Scholar
[102] O. Hrycyna, M. Szydlowski, and M. Kamionka, “Dynamics and cosmological constraints on Brans-Dicke cosmology,” Phys. Rev. D, vol. 90, p. 124040, 2014. https://doi.org/10.1103/physrevd.90.124040.Search in Google Scholar
[103] J. E. Lidsey, D. J. Mulryne, N. J. Nunes, and R. Tavakol, “Oscillatory universes in loop quantum cosmology and initial conditions for inflation,” Phys. Rev. D, vol. 70, p. 063521, 2004. https://doi.org/10.1103/physrevd.70.063521.Search in Google Scholar
[104] R. Penrose, “The basic ideas of conformal cyclic cosmology,” AIP Conf. Proc., vol. 1446, p. 233, 2012.10.1063/1.4727997Search in Google Scholar
[105] H. H. Xiong, Y.-F. Cai, T. Qiu, Y.-S. Piao, and X. Zhang, “Oscillating universe with quintom matter,” Phys. Lett. B, vol. 666, pp. 212–217, 2008. https://doi.org/10.1016/j.physletb.2008.07.053.Search in Google Scholar
[106] J. Kehayias and R. J. Scherrer, “Oscillating and static universes from a single barotropic fluid,” J. Cosmol. Astropart. Phys., vol. 12, p. 015, 2015. https://doi.org/10.1088/1475-7516/2015/12/015.Search in Google Scholar
[107] M. Rezaei, “Observational constraints on the oscillating dark energy cosmologies,” Mon. Not. Roy. Astron. Soc., vol. 485, pp. 550–559, 2019. https://doi.org/10.1093/mnras/stz394.Search in Google Scholar
[108] M. Shen and L. Zhao, “Oscillating quintom model with time periodic varying deceleration parameter,” Chin. Phys. Lett., vol. 31, p. 010401, 2014. https://doi.org/10.1088/0256-307x/31/1/010401.Search in Google Scholar
[109] P. K. Sahoo, “A periodic varying deceleration parameter in f(R, T) gravity,” Mod. Phys. Lett. A, vol. 33, p. 1850193, 2018. https://doi.org/10.1142/s0217732318501936.Search in Google Scholar
[110] D. Jain, A. Dev, and J. S. Alcaniz, “Cosmological bounds on oscillating dark energy models,” Phys. Lett. B, vol. 656, pp. 15–18, 2007. https://doi.org/10.1016/j.physletb.2007.09.023.Search in Google Scholar
© 2021 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Dynamical Systems & Nonlinear Phenomena
- Simultaneous effects of Brownian motion and thermophoretic force on Eyring–Powell fluid through porous geometry
- Gravitation & Cosmology
- A cyclic non-singular universe from Gauss–Bonnet and superstring corrections
- Hydrodynamics
- Mathematical modelling of classical Graetz–Nusselt problem for axisymmetric tube and flat channel using the Carreau fluid model: a numerical benchmark study
- Solid State Physics & Materials Science
- Enhancement of thermal conductivity and ultrasonic properties by incorporating CdS nanoparticles to PVA nanofluids
- Pressure and size dependent investigation of ultrasonic and thermal properties of ScRu intermetallic
- Thermodynamics & Statistical Physics
- Analytical treatment of the critical properties of a generalized van der Waals equation
- Thermodynamic equilibrium of a fluid column under the influence of gravity
Articles in the same Issue
- Frontmatter
- Dynamical Systems & Nonlinear Phenomena
- Simultaneous effects of Brownian motion and thermophoretic force on Eyring–Powell fluid through porous geometry
- Gravitation & Cosmology
- A cyclic non-singular universe from Gauss–Bonnet and superstring corrections
- Hydrodynamics
- Mathematical modelling of classical Graetz–Nusselt problem for axisymmetric tube and flat channel using the Carreau fluid model: a numerical benchmark study
- Solid State Physics & Materials Science
- Enhancement of thermal conductivity and ultrasonic properties by incorporating CdS nanoparticles to PVA nanofluids
- Pressure and size dependent investigation of ultrasonic and thermal properties of ScRu intermetallic
- Thermodynamics & Statistical Physics
- Analytical treatment of the critical properties of a generalized van der Waals equation
- Thermodynamic equilibrium of a fluid column under the influence of gravity