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Reconstruction of cosmic history from a simple parametrization of $H$

Shibesh Kumar Jas Pacif

Centre for Theoretical Physics, Jamia Millia Islamia, New Delhi 110025, India

E-mail Address: shibesh.math@gmail.com

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Ratbay Myrzakulov

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

E-mail Address: rmyrzakulov@gmail.com

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, and

Shynaray Myrzakul

Department of Theoretical and Nuclear Physics, Al-Farabi Kazakh National University, Al-Farabi av. 71, 050040, Almaty, Kazakhstan

E-mail Address: shynaray1981@gmail.com

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https://doi.org/10.1142/S0219887817501110Cited by:59 (Source: Crossref)

Abstract

In this paper, we propose a simple parametrization of the Hubble parameter (HP) $H$ in order to explain the late-time cosmic acceleration. We show that our proposal covers many models obtained in different schemes of parametrization under one umbrella. We demonstrate that a simple modification in the functional form of HP can give rise to interesting cosmological phenomena such as big rip singularity, bounce and others. We have also constrained the model parameters using the latest 28 points of $H (z)$ data for three cases which admit transition from deceleration to acceleration.

Keywords:

AMSC: 83F05, 83C15

References

1. A. Sandage, Cosmology: A search for two numbers, Phys. Today 23 (1970) 34. Crossref, Web of Science, Google Scholar
2. S. Perlmutter et al., Measurements of $Ω$ and $Λ$ from 42 high-redshift supernovae, Astrophys. J. 517 (1999) 565–586. Crossref, Web of Science, Google Scholar
3. A. G. Riess et al., Observational evidence from supernovae for an accelerating universe and cosmological constant, Astron. J. 116 (1998) 1009–1038. Crossref, Web of Science, Google Scholar
4. A. G. Riess et al., Tests of the accelerating universe with near-infrared observations of a high-redshift type Ia supernovae, Astrophys. J. 536 (2000) 62–74. Crossref, Web of Science, Google Scholar
5. A. G. Riess et al., New hubble space telescope discoveries of type Ia supernovae at $z > 1$ : Narrowing constraints on the early behavior of dark energy, Astrophys. J. 659 (2007) 98–121. Crossref, Web of Science, Google Scholar
6. D. H. Weinberg et al., Observational probes of cosmic acceleration, Phys. Rep. 530 (2013) 87–255. Crossref, Web of Science, Google Scholar
7. P. Astier et al., The supernovae legacy survey, Astron. Astrophys. 447 (2006) 31–48. Crossref, Web of Science, Google Scholar
8. Amanullah et al., Spectra and light curves of six type Ia supernovae at $0.511 < z < 1.12$ and the Union2 compilation, Astrophys. J. 716 (2010) 712–738. Crossref, Web of Science, Google Scholar
9. D. Rubin et al., Precision measurement of the most distant spectroscopically confirmed supernovae Ia with the Hubble space telescope, Astrophys. J. 763 (2013) 35–45. Crossref, Web of Science, Google Scholar
10. A. H. Jaffe et al., Cosmology from Maxima-1, Boomerang and Cobe DMR cosmic microwave background observations, Phys. Rev. Lett. 86 (2001) 3475–3479. Crossref, Web of Science, Google Scholar
11. D. N. Spergel et al., Wilkinson microwave anisotropy probe (WMAP) three year results: Implications for cosmology, Astrophys. J. Suppl. 170 (2007) 377–408. Crossref, Web of Science, Google Scholar
12. J. R. Bond et al., Forecasting cosmic parameter errors from microwave background anisotropy experiments, Mon. Not. R. Astron. Soc. 291 (1997) L33–L41. Web of Science, Google Scholar
13. Y. Wang and P. Mukherjee, Robust dark energy constraints from supernovae, galaxy clustering and 3 yr Wilkinson microwave anisotropy probe observations, Astrophys. J. 650 (2006) 1–6. Crossref, Web of Science, Google Scholar
14. U. Seljak et al., Cosmological parameter analysis including SDSS Ly $α$ forest and galaxy bias: Constraints on the primordial spectrum of fluctuations, neutrino mass and dark energy, Phys. Rev. D 71 (2005) 103515. Crossref, Web of Science, Google Scholar
15. J. K. Adelman-McCarthy et al., The fourth data release of the sloan digital sky survey, Astrophys. J. Suppl. 162 (2006) 38–48. Crossref, Web of Science, Google Scholar
16. R. G. Vishwakarma, Einstein and beyond: A critical perspective on general relativity, Universe 2 (2016) 11. Crossref, Web of Science, Google Scholar
17. R. G. Vishwakarma, A Machian approach to general relativity, Int. J. Geom. Methods Mod. Phys. 12 (2015) 1550116. Link, Web of Science, Google Scholar
18. R. G. Vishwakarma, Mysteries of $R_{i k} = 0$ : A novel paradigm in Einstein’s theory of gravitation, Front. Phys. 9 (2014) 98–112. Crossref, Web of Science, Google Scholar
19. R. G. Vishwakarma, Mysteries of the geometrization of gravitation, Res. Astron. Astrophys. 13 (2013) 1409–1422. Crossref, Web of Science, Google Scholar
20. V. Sahni and A. Starobinsky, The case for a positive cosmological $Λ$ -term, Int. J. Mod. Phys. D 9 (2000) 373–443. Link, Web of Science, Google Scholar
21. R. G. Vishwakarma, Consequences on some dark energy candidates from SN 1997ff, Mon. Not. R. Astron. Soc. 331 (2002) 776–784. Crossref, Web of Science, Google Scholar
22. P. J. E. Peebles and B. Ratra, The cosmological constant and dark energy, Rev. Mod. Phys. 75 (2003) 559–606. Crossref, Web of Science, Google Scholar
23. S. Weinberg, The cosmological constant problem, Rev. Mod. Phys. 61 (1989) 1–23. Crossref, Web of Science, Google Scholar
24. B. Ratra and P. J. E. Peebles, Cosmological consequences of a rolling homogeneous scalar field, Phys. Rev. D 37 (1988) 3406. Crossref, Web of Science, Google Scholar
25. R. R. Caldwell, R. Dave and P. J. Steinhardt, Cosmological imprint of an energy component with general equation of state, Phys. Rev. Lett. 80 (1998) 1582–1585. Crossref, Web of Science, Google Scholar
26. V. Sahni, M. Sami and T. Souradeep, Relic gravity waves from brane world inflation, Phys. Rev. D 65 (2002) 023518. Crossref, Web of Science, Google Scholar
27. M. Sami and T. Padmanabhan, A viable cosmology with a scalar field coupled to the trace of the stress tensor, Phys. Rev. D 67 (2003) 083509. Crossref, Web of Science, Google Scholar
28. Armendariz-Picon, T. Damour and V. Mukhanov, $k$ -inflation, Phys. Lett. B 458 (1999) 209–218. Crossref, Web of Science, Google Scholar
29. T. Chiba, T. Okabe and M. Yamaguchi, Kinetically driven quintessence, Phys. Rev. D 62 (2000) 023511. Crossref, Web of Science, Google Scholar
30. L. A. Boyle, R. R. Caldwell and M. Kamionkowski, Spintessence! New models for dark matter and dark energy, Phys. Lett. B 545 (2002) 17–22. Crossref, Web of Science, Google Scholar
31. A. Sen, Tachyon matter, J. High Energy Phys. 0207 (2002) 065. Crossref, Web of Science, Google Scholar
32. T. Padmanabhan, Accelerated expansion of the universe driven by tachyonic matter, Phys. Rev. D 66 (2002) 021301. Crossref, Web of Science, Google Scholar
33. B. Feng, X. L. Wang and X. M. Zhang, Dark energy constraints from the cosmic age and supernova: Phys. Lett. B 607 (2005) 35–41. Crossref, Web of Science, Google Scholar
34. Z. K. Guo, Y. S. Pio, Y. Z. Zhang and X. M. Zhang, Cosmological evolution of a quantom model of dark energy, Phys. Lett. B 608 (2005) 177–182. Crossref, Web of Science, Google Scholar
35. M. R. Setare, J. Sadeghi and A. R. Amani, Shape invariance method for quantom model in the bent brane background, Phys. Lett. B 660 (2008) 299–306. Crossref, Web of Science, Google Scholar
36. M. R. Setare and E. N. Saridakis, Quantom cosmology with general potentials, Int. J. Mod. Phys. D 18 (2009) 549–557. Link, Web of Science, Google Scholar
37. J. Khoury and A. Weltman, Chameleon fields: Awaiting surprises for tests of gravity in space, Phys. Rev. Lett. 93 (2004) 171104. Crossref, Web of Science, Google Scholar
38. J. Khoury and A. Weltman, Chameleon cosmology, Phys. Rev. D 69 (2004) 044026. Crossref, Web of Science, Google Scholar
39. Abdussattar and S. R. Prajapati, An exact chameleon cosmological model unifying phantom inflation with late-time acceleration, Int. J. Theor. Phys. 50 (2011) 2355–2365. Crossref, Web of Science, Google Scholar
40. L. Parker and A. Raval, Nonperturbative effects of vacuum energy on the recent expansion of the universe, Phys. Rev. D 60 (1999) 063512. Crossref, Web of Science, Google Scholar
41. V. Sahni and A. Starobinsky, The case for a positive cosmological Lambda term, Int. J. Mod. Phys. D 9 (2000) 373–444. Link, Web of Science, Google Scholar
42. S. Nojiri and S. D. Odintsov, Quantum de Sitter cosmology and phantom matter, Phys. Lett. B 562 (2003) 147–152. Crossref, Web of Science, Google Scholar
43. P. Singh, M. Sami and N. Dadhich, Cosmological dynamics of phantom field, Phys. Rev. D 68 (2003) 023522. Crossref, Web of Science, Google Scholar
44. M. Sami and A. Toporensky, Phantom field and the fate of universe, Mod. Phys. Lett. A 19 (2004) 1509. Link, Web of Science, Google Scholar
45. M. Sami et al., The fate of (phantom) dark energy universe with string curvature corrections, Phys. Lett. B 619 (2005) 193. Crossref, Web of Science, Google Scholar
46. A. Yu. Kamenshchik, U. Moschella and V. Pasquier, An alternative to quintessence, Phys. Lett. B 511 (2001) 265–268. Crossref, Web of Science, Google Scholar
47. V. Gorini et al., The Chaplygin gas, a model for dark energy in cosmology, AIP Conf. Proc. 751 (2005) 108–125. Crossref, Google Scholar
48. E. J. Copeland, M. Sami and S. Tsujikawa, Dynamics of dark energy, Int. J. Mod. Phys. D 15 (2006) 1753–1936. Link, Web of Science, Google Scholar
49. M. Sami, Why is universe so dark? New Adv. Phys. 10 (2016) 77–105. Google Scholar
50. M. Sami and R. Myrzakulov, Late time cosmic acceleration: ABCD of dark energy and modified theories of gravity, Int. J. Mod. Phys. D 25 (2016) 1630031. Link, Web of Science, Google Scholar
51. Md. Wali Hossain et al., Unification of inflation and dark energy à la quintessential inflation, Int. J. Mod. Phys. D 24 (2015) 1530014. Link, Web of Science, Google Scholar
52. M. Sami, A primer on problems and prospects of dark energy, Curr. Sci. 97 (2009) 887. Web of Science, Google Scholar
53. M. Sami, Dark energy and possible alternatives, preprint (2009), arXiv:hep-th/0901.0756. Google Scholar
54. J. Yoo and Y. Watanabe, Theoretical models of dark energy, Int. J. Mod. Phys. D 21 (2012) 1230002. Link, Web of Science, Google Scholar
55. M. S. Turner and A. G. Riess, Do SNe Ia provide direct evidence for past deceleration of the universe? Astrophys. J. 569 (2002) 18–22. Crossref, Web of Science, Google Scholar
56. S. Weinberg, Cosmology and Gravitation (John Wiley Sons, New York, 1972). Google Scholar
57. E. V. Linder, The paths of quintessence, Phys. Rev. D 73 (2006) 063010. Crossref, Web of Science, Google Scholar
58. Yu. L. Bolotin et al., Cosmology in terms of deceleration parameter. Part-I, preprint (2015), arXiv:gr-qc/1502.00811. Google Scholar
59. Yu. L. Bolotin et al., Cosmology in terms of deceleration parameter. Part-II, preprint (2015), arXiv:gr-qc/1506.08918. Google Scholar
60. S. Nojiri, S. D. Odintsov and V. K. Oikonomou, Singular inflation from generalized equation of state fluids, Phys. Lett. B 747 (2015) 310–320. Crossref, Web of Science, Google Scholar
61. M. S. Berman, Special law of variation for Hubble’s parameter, Nuovo Cimento B 74 (1983) 182–186. Crossref, Web of Science, Google Scholar
62. N. Banerjee, S. Das and K. Ganguly, Chameleon field and the late time acceleration of the universe, Pramana 74 (2010) L481–L489. Crossref, Web of Science, Google Scholar
63. J. P. Singh, A cosmological model with both deceleration and acceleration, Astrophys. Space Sci. 318 (2008) 103–107. Crossref, Web of Science, Google Scholar
64. S. K. J. Pacif and B. Mishra, FLRW non-singular cosmological model in general relativity, Res. Astron. Astrophys. 15 (2015) 2141–2150. Crossref, Web of Science, Google Scholar
65. S. K. J. Pacif and B. Mishra, Anisotropic cosmological model with a specific form of Hubble parameter, Astrophys. Space Sci. 360 (2015) 48–53. Crossref, Web of Science, Google Scholar
66. F. Cannata and A. Y. Kamenshchik, Chameleon cosmology model describing the phantom divide line crossing, Int. J. Mod. Phys. D 20 (2011) 121–131. Link, Web of Science, Google Scholar
67. S. Noniri and S. D. Odintsov, Unifying phantom inflation with late-time acceleration: Scalar phantom-non-phantom transition model and generalized holographic dark energy, Gen. Relativ. Gravit. 38 (2006) 1285–1304. Crossref, Web of Science, Google Scholar
68. P. H. Frampton et al., Models for little rip dark energy, Phys. Lett. B 708 (2012) 204–211. Crossref, Web of Science, Google Scholar
69. S. Nojiri et al., Singular cosmological evolution using canonical and ghost scalar fields, J. Cosmol. Astropart. Phys. 1509 (2015) 044. Crossref, Google Scholar
70. K. Bamba et al., Bouncing cosmology in modified Gauss–Bonnet gravity, Phys. Lett. B 732 (2014) 349–355. Crossref, Web of Science, Google Scholar
71. D. Lohiya and M. Sethi, A program for a problem free cosmology within a framework of a rich class of scalar tensor theories, Class. Quantum Grav. 16 (1999) 1545–1563. Crossref, Web of Science, Google Scholar
72. M. S. Berman, Cosmological models with a variable cosmological term, Phys. Rev. D 43 (1991) 1075–1078. Crossref, Web of Science, Google Scholar
73. A.-M. M. Abdel Rahman, Singularity-free decaying-vacuum cosmologies, Phys. Rev. D 45 (1992) 3497–3511. Crossref, Web of Science, Google Scholar
74. Abdussattar and S. R. Prajapati, Role of deceleration parameter and interacting dark energy in singularity avoidance, Astrophys. Space Sci. 331 (2011) 657–663. Crossref, Web of Science, Google Scholar
75. O. Akarsu and T. Dereli, Cosmological models with linearly varying deceleration parameter, Int. J. Theoret. Phys. 51 (2012) 612–621. Crossref, Web of Science, Google Scholar
76. O. Akarsu et al., Cosmology with hybrid expansion law: Scalar field reconstruction of cosmic history and observational constraints, J. Cosmol. Astropart. Phys. 1401 (2014) 022. Crossref, Web of Science, Google Scholar
77. B. Mishra and S. K. Tripathy, Anisotropic dark energy model with a hybrid scale factor, Mod. Phys. Lett. A 30 (2015) 1550175. Link, Web of Science, Google Scholar
78. J. M. Overduin and F. I. Cooperstock, Evolution of the scale factor with a variable cosmological term, Phys. Rev. D 58 (1998) 043506. Crossref, Web of Science, Google Scholar
79. R. G. Vishwakarma, Is the present expansion of the universe really accelerating? Mon. Not. R. Astron. Soc. 345 (2003) 545–551. Crossref, Web of Science, Google Scholar
80. J. Simon et al., Constraints on the redshift dependence of the dark energy potential, Phys. Rev. D 71 (2005) 123001. Crossref, Web of Science, Google Scholar
81. M. Moresco et al., Improved constraints on the expansion rate of the universe up to $z \sim 1.1$ from the spectroscopic evolution of cosmic chronometers, J. Cosmol. Astropart. Phys. 1208 (2012) 006. Crossref, Web of Science, Google Scholar
82. J. A. Cuesta et al., The clustering of galaxies in the SDSS-III baryon oscillation spectroscopic survey: Baryon acoustic oscillations in the correlation function of LOWZ and CMASS galaxies in data release 12, Mon. Not. R. Astron. Soc. 457 (2016) 1770–1785. Crossref, Web of Science, Google Scholar
83. C. Blake et al., The wiggleZ dark energy survey: Joint measurements of the expansion and growth history at $z < 1$ , Mon. Not. R. Astron. Soc. 425 (2012) 405. Crossref, Web of Science, Google Scholar
84. D. Stern et al., Cosmic chronometers: Constraining the equation of state of dark energy. I: $H (z)$ measurements, J. Cosmol. Astropart. Phys. 1002 (2010) 008. Crossref, Web of Science, Google Scholar
85. M. Moresco et al., A 6% measurement of the Hubble parameter at $z \sim 0.45$ direct evidence of the epoch of cosmic re-acceleration, J. Cosmol. Astropart. Phys. 1605 (2016) 014. Crossref, Web of Science, Google Scholar
86. T. Delubac et al., Baryon acoustic oscillations in the Ly $α$ forest of BOSS DR11 quasars, Astron. Astrophys. 574 (2015) A59. Crossref, Web of Science, Google Scholar
87. A. Font-Ribera et al., Quasar–Lyman $α$ forest cross-correlation from BOSS DR11: Baryon acoustic oscillations, J. Cosmol. Astropart. Phys. 1405 (2014) 027. Crossref, Web of Science, Google Scholar
88. M. Sethi, A. Batra and D. Lohiya, On ‘observational constraints on power-law cosmology’, Phys. Rev. D 60 (1999) 108301. Crossref, Web of Science, Google Scholar
89. G. F. R. Ellis and M. S. Madsen, Exact scalar field cosmologies, Class. Quantum Grav. 8 (1991) 667–676. Crossref, Web of Science, Google Scholar
90. S. D. Odintsov and V. K. Oikonomou, Bouncing cosmology with future singularity from modified gravity, Phys. Rev. D 92 (2015) 024016. Crossref, Web of Science, Google Scholar
91. S. Nojiri, S. D. Odintsov and S. Tsujikawa, Properties of singularities in the (phantom) dark energy universe, Phys. Rev. D 71 (2005) 063004. Crossref, Web of Science, Google Scholar
92. M. Ozer and M. O. Taha, A solution to the main cosmological problems, Phys. Lett. B 171 (1986) 363–365. Crossref, Web of Science, Google Scholar
93. M. Ozer and M. O. Taha, A model of the universe with time dependent cosmological constant free of cosmological problems, Nucl. Phys. B 287 (1987) 776. Crossref, Web of Science, Google Scholar
94. A.-M. M. Abdel-Rahman, A critical density cosmological model with varying gravitational and cosmological “constants”, Gen. Relativ. Gravit. 22 (1990) 655. Crossref, Web of Science, Google Scholar
95. S. K. J. Pacif and Abdussattar, On the simultaneous variation of some cosmological parameters in the presence of interacting dark energy, Eur. Phys. J. Plus 129 (2014) 244. Crossref, Web of Science, Google Scholar
96. S. K. J. Pacif and Abdussattar, On simultaneous variation of some cosmological parameters, in Proc. Int. Conf. “Innovative Approach in Applied Physical, Mathematical/Statistical, Chemical Sciences and Emerging Energy Technology for Sustainable Development” (Krishi Sanskriti Publications, New Delhi, India, 2014), pp. 69–74. Google Scholar
97. J. N. Islam, An Introduction to Mathematical Cosmology (Cambridge University Press, UK, 1992). Google Scholar
98. Abdussattar and S. R. Prajapati, Friedman–Robertson–Walker models with late-time acceleration, Chin. Phys. Lett. 28 (2011) 029803. Crossref, Web of Science, Google Scholar
99. Abdussattar and R. G. Vishwakarma, A model of the universe with decaying vacuum energy, Pramana 47 (1996) 41–55. Crossref, Web of Science, Google Scholar
100. R. G. Vishwakarma, Study of the magnitude redshift relation for type Ia supernovae in a model resulting from Ricci symmetry, Gen. Relativ. Grav. 33 (2001) 1973–1984. Crossref, Web of Science, Google Scholar
101. R. G. Vishwakarma, Abdussattar and A. Beesham, LRS bianchi-type I models with a time dependent cosmological ‘Constant’, Phys. Rev. D 60 (1999) 063507. Crossref, Web of Science, Google Scholar
102. Abdussattar and R. G. Vishwakarma, Some Robertson–Walker models with variable $G$ and Lambda, Aust. J. Phys. 50 (1997) 893–901. Crossref, Google Scholar
103. T. S. Olson and T. F. Jordan, Ages of the universe for decreasing cosmological constants, Phys. Rev. D 35 (1987) 3258. Crossref, Web of Science, Google Scholar
104. D. Pavon, Nonequillibrium fluctuations in cosmic vacuum decay, Phys. Rev. D 43 (1991) 375. Crossref, Web of Science, Google Scholar
105. R. G. Vishwakarma, Consequences on variable $39 b$ -models from distant type Ia supernovae and compact radio sources, Class. Quantum Grav. 18 (2001) 1159. Crossref, Web of Science, Google Scholar
106. S. Ray et al., Scenario of inflationary cosmology from the phenomenological $Λ$ models, Int. J. Theor. Phys. 48 (2009) 2499. Crossref, Web of Science, Google Scholar
107. A. I. Arbab, Cosmological models with variable cosmological and gravitational constants and bulk viscous models, Gen. Relativ. Gravit. 29 (1997) 61–74. Crossref, Web of Science, Google Scholar
108. A. I. Arbab, Phantom energy with variable $G$ and Lambda, Chin. Phys. Lett. 25 (2008) 4497–4500. Crossref, Web of Science, Google Scholar
109. S. G. Rajeev, Why is the cosmological constant small? Phys. Lett. B 125 (1983) 144–146. Crossref, Web of Science, Google Scholar
110. A. D. Linde, Is the Lee constant a cosmological constant? JETP Lett. 19 (1974) 183. Web of Science, Google Scholar
111. A. Beesham, Cosmological models with a variable cosmological term and bulk viscous models, Phys. Rev. D 48 (1993) 3539–3543. Crossref, Web of Science, Google Scholar
112. J. C. Carvalho, J. A. S. Lima and I. Waga, On the cosmological consequences of a time dependent lambda term, Phys. Rev. D 46 (1992) 2404–2407. Crossref, Web of Science, Google Scholar
113. A. I. Arbab and A.-M. M. Abdel-Rahman, Nonsingular cosmology with a time dependent cosmological term, Phys. Rev. D 50 (1994) 7725–7728. Crossref, Web of Science, Google Scholar
114. A. S. Al-Rawaf, Cosmological consequences of a model with a generalized cosmological constant, Mod. Phys. Lett. A 14 (1999) 1157–1161. Link, Web of Science, Google Scholar
115. A. I. Arbab, FRW type universe with vacuum energy density, Gravit. Cosmol. 8 (2002) 227–231. Google Scholar
116. J. W. Moffat, Lagrangian formulation of a solution to the cosmological constant problem, preprint (1996), arXiv:astro-ph/9608202. Google Scholar
117. C. Ekart, The thermodynamics of irreversible processes. III. Relativistic theory of the simple fluid, Phys. Rev. D 58 (1940) 919. Crossref, Google Scholar
118. O. Gron, Viscous inflationary universe models, Astrophys. Space Sci. 173 (1990) 191–225. Crossref, Web of Science, Google Scholar
119. S. Nojiri and S. D. Odintsov, Final state and thermodynamics of a dark energy universe, Phys. Rev. D 70 (2004) 103522. Crossref, Web of Science, Google Scholar
120. K. Karami, S. Ghaffari and J. Fehri, Interacting polytropic gas model of phantom dark energy in non-flat universe, Eur. Phys. J. C 64 (2009) 85–88. Crossref, Web of Science, Google Scholar
121. P.-H. Chavanis, Models of universe with a polytropic equation of sate: I. The early universe, Eur. Phys. J. Plus 129 (2014) 38. Crossref, Web of Science, Google Scholar
122. P.-H. Chavanis, A cosmological model describing the early inflation, the intermediate decelerating expansion and the late accelerating expansion of the universe by a quadratic equation of state, Universe 1 (2015) 357–411. Crossref, Web of Science, Google Scholar
123. M. C. Bento, O. Bertolami and A. A. Sen, Generalized Chaplygin gas, accelerated expansion and dark energy-matter unification, Phys. Rev. D 66 (2002) 043507. Crossref, Web of Science, Google Scholar
124. V. Gorini, A. Yu. Kamenshchik and U. Moschella, Can the Chaplygin gas be a plausible model for dark energy? Phys. Rev. D 67 (2003) 063509. Crossref, Web of Science, Google Scholar
125. H. B. Benaoum, Accelerated universe from modified Chaplygin gas and tachyonic fluid, preprint (2002), arXiv:hep-th/0205140. Google Scholar
126. U. Debnath, A. Banerjee and S. Chakraborty, Role of modified Chaplygin gas in accelerated universe, Class. Quantum Grav. 21 (2004) 5609–5618. Crossref, Web of Science, Google Scholar
127. U. Debnath, Variable modified Chaplygin gas and accelerating universe, Astrophys. Space Sci. 312 (2007) 295–299. Crossref, Web of Science, Google Scholar
128. W. Chakraborty and U. Debnath, A new variable modified Chaplygin gas model interacting with scalar field, Gravit. Cosmol. 16 (2010) 223–227. Crossref, Web of Science, Google Scholar
129. N. Banerjee and S. Das, Acceleration of the universe with a simple trigonometric potential, Gen. Relativ. Gravit. 37 (2005) 1695–1703. Crossref, Web of Science, Google Scholar
130. A. G. Riess et al., Type Ia supernovae discoveries at $z > 1$ from the Hubble space telescope: Evidence for past deceleration and constraints on dark energy evolution, Astrophys. J. 607 (2004) 665–687. Crossref, Web of Science, Google Scholar
131. J. V. Chuna and J. A. S. Lima, Mon. Not. R. Astron. Soc. 390 (2008) 210. Crossref, Web of Science, Google Scholar
132. J. V. Cunha, Kinematic constraints to the transition redshift from supernovae type Ia union data, Phys. Rev. D 79 (2009) 047301. Crossref, Web of Science, Google Scholar
133. R. Nair et al., Cosmokinetics: A joint analysis of standard candles, rulers and cosmic clocks, J. Cosmol. Astropart. Phys. 1201 (2012) 018. Crossref, Web of Science, Google Scholar
134. B. Santos, J. C. Carvalho and J. S. Alcaniz, Current constraints on the epoch of cosmic acceleration, Astropart. Phys. 35 (2011) 17–20. Crossref, Web of Science, Google Scholar
135. L. Xu and H. Liu, Constraints to deceleration parameters by recent cosmic observations, Mod. Phys. Lett. A 23 (2008) 1939. Link, Web of Science, Google Scholar
136. A. Al Mamon and S. Das, A divergence free parametrization of deceleration parameter for scalar field dark energy, preprint (2015), arXiv:gr-qc/1507.00531v1. Google Scholar
137. Y. G. Gong and A. Wang, Observational constraints on the acceleration of the universe, Phys. Rev. D 73 (2006) 083506. Crossref, Web of Science, Google Scholar
138. J. Lu, L. Xu and M. Liu, Constraints on kinematic models from the latest observational data, Phys. Lett. B 699 (2011) 246–250. Crossref, Web of Science, Google Scholar
139. Y. G. Gong and A. Wang, Reconstruction of the deceleration parameter and the equation of state of dark energy, Phys. Rev. D 75 (2007) 043520. Crossref, Web of Science, Google Scholar
140. S. del Campo et al., Three thermodynamically based parametrizations of the deceleration parameter, Phys. Rev. D 86 (2012) 083509. Crossref, Web of Science, Google Scholar
141. D. Pavon et al., Parameterizing the deceleration parameter, in Proc. MG13 Meeting on General Relativity Stockholm University (World Scientific Publication Co., Europe, 2012), pp. 1564–1566. Google Scholar
142. D. Huterer and M. S. Turner, Probing dark energy: Methods and strategies, Phys. Rev. D 64 (2001) 123527. Crossref, Web of Science, Google Scholar
143. J. Weller and A. Albrecht, Future supernovae observations as a probe of dark energy, Phys. Rev. D 65 (2002) 103512. Crossref, Web of Science, Google Scholar
144. H. K. Jassal, J. S. Bagla and T. Padmanabhan, WMAP constraints on low redshift evolution of dark energy, Mon. Not. R. Astron. Soc. Lett. 356 (2005) L11–L16. Crossref, Web of Science, Google Scholar
145. M. Chevallier and D. Polarski, Accelerating universes with scaling dark matter, Int. J. Mod. Phys. D 10 (2001) 213–224. Link, Web of Science, Google Scholar
146. E. V. Linder, Exploring the expansion history of the universe, Phys. Rev. Lett. 90 (2003) 091301. Crossref, Web of Science, Google Scholar
147. G. Pantazis, S. Nesseris and L. Perivolaropoulos, Comparison of thawing and freezing dark energy parametrizations, Phys. Rev. D 93 (2016) 103503. Crossref, Web of Science, Google Scholar
148. E. M. Barboza, Jr. and J. S. Alcaniz, Probing the time dependence of dark energy, J. Cosmol. Astropart. Phys. 1202 (2012) 042. Crossref, Web of Science, Google Scholar
149. C.-J. Feng et al., A new class of parametrization for dark energy without divergence, J. Cosmol. Astropart. Phys. 1209 (2012) 023. Crossref, Web of Science, Google Scholar
150. R. Lazkoz, V. Salzano and I. Sendra, Oscillations in the dark energy EoS: New MCMC lessons, Phys. Lett. B 694 (2011) 198–208. Crossref, Web of Science, Google Scholar
151. G. Efstathiou, Constraining the equation of state of the universe from distant type Ia supernovae and cosmic microwave background anisotropies, Mon. Not. R. Astron. Soc. 310 (1999) 842–850. Crossref, Web of Science, Google Scholar
152. J.-Z. Ma and X. Zhang, Probing the dynamics of dark energy with novel parametrizations, Phys. Lett. B 699 (2011) 233–238. Crossref, Web of Science, Google Scholar
153. D.-J. Liu et al., Revisiting the parametrization of equation of state of dark energy via SNIa data, Mon. Not. R. Astron. Soc. 388 (2008) 275–281. Crossref, Web of Science, Google Scholar
154. L. Feng and T. Lu, A new equation of state for dark energy model, J. Cosmol. Astropart. Phys. 11 (2011) 034. Crossref, Web of Science, Google Scholar