Table of Contents Author Guidelines Submit a Manuscript
Advances in High Energy Physics
Volume 2017, Article ID 1424503, 11 pages
https://doi.org/10.1155/2017/1424503
Research Article

A Thermodynamic Approach to Holographic Dark Energy

Orlando Luongo1,2,3,4,5

1Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, Cape Town 7701, South Africa
2Astrophysics, Cosmology and Gravity Centre (ACGC), University of Cape Town, Rondebosch, Cape Town 7701, South Africa
3School of Science and Technology, University of Camerino, 62032 Camerino, Italy
4Dipartimento di Fisica, Università di Napoli “Federico II”, Via Cinthia, 80126 Napoli, Italy
5Istituto Nazionale di Fisica Nucleare (INFN), Sez. di Napoli, Via Cinthia 9, 80126 Napoli, Italy

Correspondence should be addressed to Orlando Luongo; ti.nfni.an@ognoul

Received 31 December 2016; Revised 9 March 2017; Accepted 20 April 2017; Published 30 July 2017

Academic Editor: Burak Bilki

Copyright © 2017 Orlando Luongo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Linked References

  1. A. G. Riess, A. V. Filippenko, P. Challis, and A. Clocchiattia et al., “Observational evidence from supernovae for an accelerating universe and a cosmological constant,” The Astronomical Journal, vol. 116, no. 3, pp. 1009–1038, 1998. View at Publisher · View at Google Scholar
  2. S. Perlmutter, G. Aldering, G. Goldhaber, and R. A. Knop et al., “Measurements of Ω and Λ from 42 high-redshift supernovae,” The Astrophysical Journal, vol. 517, no. 2, pp. 565–586, 1999. View at Publisher · View at Google Scholar
  3. P. Astier, “The expansion of the universe observed with supernovae,” Reports on Progress in Physics, vol. 75, no. 11, Article ID 116901, 2012. View at Publisher · View at Google Scholar
  4. P. M. Garnavich, S. Jha, P. Challis, A. Clocchiatti, A. Diercks, and A. V. Filippenko et al., “Supernova Limits on the Cosmic Equation of State,” The Astrophysical Journal, vol. 509, no. 1, pp. 74–79, 1998. View at Publisher · View at Google Scholar
  5. S. Capozziello, V. F. Cardone, E. Elizalde, S. Nojiri, and S. D. Odintsov, “Observational constraints on dark energy with generalized equations of state,” Physical Review D, vol. 73, no. 4, Article ID 043512, 2006. View at Publisher · View at Google Scholar · View at Scopus
  6. U. Seljak, A. Makarov, P. McDonald, and S. F. Anderson et al., “Cosmological parameter analysis including SDSS Lyα forest and galaxy bias: constraints on the primordial spectrum of fluctuations, neutrino mass, and dark energy,” Physical Review D, vol. 71, Article ID 103515, May 2005. View at Publisher · View at Google Scholar
  7. M. Tegmark, D. J. Eisenstein, M. A. Strauss et al., “Cosmological constraints from the SDSS luminous red galaxies,” Physical Review D, vol. 74, Article ID 123507, 2006. View at Publisher · View at Google Scholar
  8. L. Christodoulou, C. Eminian, J. Loveday, P. Norberg, and I. K. Baldry, “Galaxy and mass assembly (GAMA): colour- and luminosity-dependent clustering from calibrated photometric redshifts,” Monthly Notices of the Royal Astronomical Society, vol. 425, no. 2, pp. 1527–1548, 2012. View at Publisher · View at Google Scholar
  9. W. J. Percival, S. Cole, D. J. Eisenstein et al., “Measuring the baryon acoustic oscillation scale using the sloan digital sky survey and 2dF galaxy redshift survey,” Monthly Notices of the Royal Astronomical Society, vol. 381, no. 3, pp. 1053–1066, 2007. View at Publisher · View at Google Scholar
  10. S. M. Carroll, “Why is the universe accelerating?” AIP Conference Proceedings, vol. 743, no. 1, pp. 16–32, 2005. View at Publisher · View at Google Scholar
  11. R. Amanullah, C. Lidman, D. Rubin, G. Aldering, P. Astier et al., “Spectra and hubble space telescope light curves of six type ia supernovae at 0.511 < z < 1.12 and the union2 compilation,” The Astrophysical Journal, vol. 716, no. 1, pp. 712–738, 2010. View at Publisher · View at Google Scholar
  12. V. Sahni and A. Starobinsky, “Reconstructing dark energy,” International Journal of Modern Physics D, vol. 15, no. 12, pp. 2105–2132, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  13. G. B. Zhao, R. G. Crittenden, L. Pogosian, and X. Zhang, “Examining the evidence for dynamical dark energy,” Physical Review Letters, vol. 109, Article ID 171301, 5 pages, 2012. View at Publisher · View at Google Scholar
  14. C. Clarkson, G. Ellis, J. Larena, and O. Umeh, “Does the growth of structure affect our dynamical models of the Universe? The averaging, backreaction, and fitting problems in cosmology,” Reports on Progress in Physics, vol. 74, no. 11, Article ID 112901, 17 pages, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  15. T. Clifton, K. Rosquist, and R. Tavakol, “An exact quantification of backreaction in relativistic cosmology,” Physical Review D, vol. 86, Article ID 043506, 2012. View at Publisher · View at Google Scholar
  16. E. W. Kolb, S. Matarrese, A. Notari, and A. Riotto, “Effect of inhomogeneities on the expansion rate of the Universe,” Physical Review D, vol. 71, Article ID 023524, 2005. View at Publisher · View at Google Scholar
  17. E. W. Kolb, “Backreaction of inhomogeneities can mimic dark energy,” Classical and Quantum Gravity, vol. 28, no. 16, Article ID 164009, 2011. View at Publisher · View at Google Scholar
  18. O. Umeh, J. Larena, and C. Clarkson, “The Hubble rate in averaged cosmology,” Journal of Cosmology and Astroparticle Physics, vol. 1103, no. 3, article 029, 12 pages, 2011. View at Publisher · View at Google Scholar
  19. E. R. Siegel and J. N. Fry, “The effects of inhomogeneities on cosmic expansion,” The Astrophysical Journal Letters, vol. 628, no. L1, 2005. View at Publisher · View at Google Scholar
  20. S. Rasanen, “Accelerated expansion from structure formation,” Journal of Cosmology and Astroparticle Physics, vol. 611, no. 11, article 003, 44 pages, 2006. View at Publisher · View at Google Scholar
  21. P. Bull and T. Clifton, “Local and nonlocal measures of acceleration in cosmology,” Physical Review D, vol. 85, Article ID 103512, 2012. View at Publisher · View at Google Scholar
  22. M. Carrera and D. Giulini, “Influence of global cosmological expansion on local dynamics and kinematics,” Reviews of Modern Physics, vol. 82, no. 1, pp. 169–208, 2010. View at Publisher · View at Google Scholar
  23. T. Padmanabhan, “Statistical mechanics of gravitating systems,” Physics Reports, vol. 188, no. 5, pp. 285–362, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  24. M. Li, X.-D. Li, S. Wang, and Y. Wang, “Dark energy,” Communications in Theoretical Physics, vol. 56, no. 3, p. 525, 2011. View at Publisher · View at Google Scholar
  25. K. Bamba, S. Capozziello, S. Nojiri, and S. D. Odintsov, “Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests,” Astrophysics and Space Science, vol. 342, no. 1, pp. 155–228, 2012. View at Publisher · View at Google Scholar
  26. L. Xu, “Constraints on the holographic dark energy model via type Ia supernovae, baryon acoustic oscillation, and WMAP7,” Physical Review D, vol. 85, Article ID 123505, 2012. View at Google Scholar
  27. Y. Che and B. Ratra, “Hubble parameter data constraints on dark energy,” Physics Letters B, vol. 703, no. 4, pp. 406–411, 2011. View at Publisher · View at Google Scholar
  28. O. Farooq and B. Ratra, “Hubble parameter measurement constraints on the cosmological deceleration-acceleration transition redshift,” The Astrophysical Journal Letters, vol. 766, no. 1, article L7, 2013. View at Publisher · View at Google Scholar
  29. J. Einasto, “Large scale structure of the universe,” AIP Conference Proceedings, vol. 1205, pp. 72–81, 2010. View at Publisher · View at Google Scholar
  30. A. E. Erkoca, M. H. Reno, and I. Sarcevic, “Probing dark matter models with neutrinos from the Galactic center,” Physical Review D, vol. 82, Article ID 113006, 2010. View at Publisher · View at Google Scholar
  31. S. Colafrancesco, “Dark matter in modern cosmology,” AIP Conference Proceedings, vol. 1206, pp. 5–26, 2010. View at Publisher · View at Google Scholar
  32. J. L. Feng, “Dark matter candidates from particle physics and methods of detection,” Annual Review of Astronomy and Astrophsics, vol. 48, pp. 495–545, 2010. View at Publisher · View at Google Scholar
  33. A. Aviles and J. L. Cervantes-Cota, “Dark degeneracy and interacting cosmic components,” Physical Review D, vol. 84, no. 8, Article ID 083515, 2011. View at Publisher · View at Google Scholar
  34. T. Clemson, K. Koyama, G.-B. Zhao, R. Maartens, and J. Väliviita, “Interacting dark energy: constraints and degeneracies,” Physical Review D, vol. 85, no. 4, Article ID 043007, 12 pages, 2012. View at Publisher · View at Google Scholar
  35. C. Bonvin, R. Durrer, and M. Kunz, “Dipole of the luminosity distance: a direct measure of H(z),” Physical Review Letters, vol. 96, Article ID 191302, 2006. View at Publisher · View at Google Scholar
  36. E. Di Dio and R. Durrer, “Vector and tensor contributions to the luminosity distance,” Physical Review D, vol. 86, Article ID 023510, 14 pages, 2012. View at Publisher · View at Google Scholar
  37. A. Albrecht, G. Bernstein, R. Cahn, W. L. Freedman, and J. Hewitt, “Report of the dark energy task force,” The Astrophysical Journal, 2006. View at Google Scholar
  38. J. Yoo and Y. Watanabe, “Theoretical models of dark energy,” International Journal of Modern Physics D, vol. 21, no. 12, Article ID 1230002, 53 pages, 2012. View at Publisher · View at Google Scholar
  39. S. Camera, C. Carbone, and L. Moscardini, “Inclusive constraints on unified dark matter models from future large-scale surveys,” Journal of Cosmology and Astroparticle Physic, vol. 2012, no. 3, article 039, 2012. View at Publisher · View at Google Scholar
  40. A. Torres-Rodriguez and C. M. Cress, “Constraining the nature of dark energy using the SKA,” Monthly Notices of the Royal Astronomical Society, vol. 376, pp. 1831–1837, 2007. View at Publisher · View at Google Scholar
  41. P. S. Corasaniti, T. Giannantonio, and A. Melchiorri, “Constraining dark energy with cross-correlated CMB and Large Scale Structure data,” Physical Review D, vol. 71, Article ID 123521, 2005. View at Publisher · View at Google Scholar
  42. A. Cabre, E. Gaztañaga, M. Manera, P. Fosalba, and F. Castander, “Cross-correlation of wilkinson microwave anisotropy probe third-year data and the sloan digital sky survey dr4 galaxy survey: new evidence for dark energy,” Monthly Notices of the Royal Astronomical Society, vol. 372, no. 1, pp. L23–L27, 2006. View at Publisher · View at Google Scholar
  43. I. Maor and O. Lahav, “On virialization with dark energy,” Journal of Cosmology and Astroparticle Physics, vol. 507, article 003, 2005. View at Google Scholar
  44. S. Lee and K.-W. Ng, “Spherical collapse model with non-clustering dark energy,” Journal of Cosmology and Astroparticle Physics, vol. 1010, article 028, 2010. View at Publisher · View at Google Scholar
  45. S. Weinberg, Cosmology, Oxford University Press, New York, NY, USA, 2008. View at MathSciNet
  46. E. Komatsu, K. M. Smith, J. Dunkley, C. L. Bennett, B. Gold, G. Hinshaw et al., “Seven-year wilkinson microwave anisotropy probe (WMAP) observations: cosmological interpretation,” The Astrophysical Journal Supplement, vol. 192, no. 2, article 18, p. 47, 2011. View at Publisher · View at Google Scholar
  47. S. Tsujikawa, “Dark energy: investigation and modeling,” in Dark Matter and Dark Energy, vol. 370 of series Astrophysics and Space Science Library, pp. 331–402, 2010. View at Publisher · View at Google Scholar
  48. Z.-X. Zhai, T.-J. Zhang, and W.-B. Liu, “Constraints on Λ(t) CDM models as holographic and agegraphic dark energy with the observational Hubble parameter data,” Journal of Cosmology and Astroparticle Physics, vol. 2011, article 019, 2011. View at Publisher · View at Google Scholar
  49. L. Lombriser, “Consistency check of ΛCDM phenomenology,” Physical Review D, vol. 83, no. 6, Article ID 063519, 2011. View at Publisher · View at Google Scholar
  50. S. Weinberg, “The cosmological constant problem,” Reviews of Modern Physics, vol. 61, no. 1, pp. 1–23, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  51. E. J. Copeland, M. Sami, and S. Tsujikawa, “Dynamics of dark energy,” International Journal of Modern Physics. D. Gravitation, Astrophysics, Cosmology, vol. 15, no. 11, pp. 1753–1935, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  52. T. P. Sotiriou and V. Faraoni, “f(R) theories of gravity,” Reviews of Modern Physics, vol. 82, no. 1, pp. 451–497, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  53. S. Capozziello and M. De Laurentis, “Extended theories of gravity,” Physics Reports, vol. 509, no. 4-5, pp. 167–321, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  54. S. Capozziello and M. Francaviglia, “Extended theories of gravity and their cosmological and astrophysical applications,” General Relativity and Gravitation, vol. 40, no. 2-3, pp. 357–420, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  55. S. Capozziello, “Curvature quintessence,” International Journal of Modern Physics D, vol. 11, no. 4, pp. 483–492, 2002. View at Publisher · View at Google Scholar
  56. T. Katsuragawa and S. Matsuzaki, “Dark matter in modified gravity?” Physical Review D, vol. 95, 4, Article ID 044040, 2017. View at Publisher · View at Google Scholar
  57. K. Bamba, “Thermodynamic properties of modified gravity theories,” International Journal of Geometric Methods in Modern Physics, vol. 13, no. 6, 1630007, 23 pages, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  58. S. Nojiri and S. D. Odintsov, “Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models,” Physics Reports, vol. 505, no. 2–4, pp. 59–144, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  59. S. Nojiri, S. Odintsov, and V. Oikonomou, “Modified gravity theories on a nutshell: Inflation, bounce and late-time evolution,” Physics Reports, https://arxiv.org/abs/1705.11098. View at Publisher · View at Google Scholar
  60. R. Bousso, “The holographic principle,” Reviews of Modern Physics, vol. 74, no. 3, pp. 825–874, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  61. S. Nojiri and S. D. Odintsov, “Unifying phantom inflation with late-time acceleration: scalar phantom–non-phantom transition model and generalized holographic dark energy,” General Relativity and Gravitation, vol. 38, no. 8, pp. 1285–1304, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  62. M. Li, X.-D. Li, S. Wang, and X. Zhang, “Holographic dark energy models: a comparison from the latest observational data,” Journal of Cosmology and Astroparticle Physics, vol. 2009, no. 6, 36 pages, 2009. View at Publisher · View at Google Scholar · View at Scopus
  63. M. Li, X.-D. Li, S. Wang, Y. Wang, and X. Zhang, “Probing interaction and spatial curvature in the holographic dark energy model,” Journal of Cosmology and Astroparticle Physics, vol. 2009, no. 12, 14 pages, 2009. View at Google Scholar
  64. S. Wang, Y. Wang, and M. Li, “Holographic dark energy,” Physics Reports, 2017, https://arxiv.org/abs/1612.00345. View at Publisher · View at Google Scholar
  65. Z. Chang, F. Q. Wu, and X. Zhang, “Constraints on holographic dark energy from X-ray gas mass fraction of galaxy clusters,” Physics Letters B, vol. 633, no. 1, pp. 14–18, 2006. View at Publisher · View at Google Scholar
  66. B. Wang, C. Y. Lin, and E. Abdalla, “Constraints on the interacting holographic dark energy model,” Physics Letters B, vol. 637, no. 6, pp. 357–361, 2006. View at Publisher · View at Google Scholar
  67. O. Luongo, L. Bonanno, and G. Iannone, “Second-order invariants and holography,” International Journal of Modern Physics D, vol. 21, no. 12, 1250091, 15 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  68. I. F. Silvera, “Bose–einstein condensation,” American Journal of Physics, vol. 65, no. 6, p. 570, 1997. View at Publisher · View at Google Scholar
  69. K. Huang, Statistical Mechanics, John Wiley and Sons, New York, NY, USA, 2nd edition, 1987. View at MathSciNet
  70. R. K. Pathria, Statistical Mechanics, International series of monographs in natural philosophy, 45, Pergamon Press, Oxford, England, 1977.
  71. Z. Yan, “General thermal wavelength and its applications,” European Journal of Physics, vol. 21, no. 6, p. 625, 2000. View at Publisher · View at Google Scholar
  72. M. Brilenkov, M. Eingorn, and A. Zhuk, “Lattice universe: examples and problems,” European Physical Journal C, vol. 75, p. 217, 2015. View at Publisher · View at Google Scholar · View at Scopus
  73. E. Bianchi, L. Hackl, and N. Yokomizo, “Entanglement entropy of squeezed vacua on a lattice,” Physical Review D, vol. 92, no. 8, 085045, 20 pages, 2015. View at Google Scholar · View at MathSciNet
  74. R. G. Liu, “Lindquist-wheeler formulation of lattice universes,” Physical Review D, vol. 92, Article ID 063529, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  75. J.-P. Bruneton and J. Larena, “Observables in a lattice universe: the cosmological fitting problem,” Classical and Quantum Gravity, vol. 30, no. 2, 025002, 19 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  76. M. Villata, “On the nature of dark energy: the lattice universe,” Astrophysics and Space Science, vol. 345, pp. 1–9, 2013. View at Publisher · View at Google Scholar
  77. S. Gielen and D. Oriti, “Quantum cosmology from quantum gravity condensates: cosmological variables and lattice-refined dynamics,” New Journal of Physics, vol. 16, Article ID 123004, 11 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  78. A. Yamamoto, “Lattice QCD in curved spacetimes,” Physical Review D, vol. 90, no. 5, Article ID 054510, 2014. View at Publisher · View at Google Scholar
  79. Y. Ling, C. Niu, J.-P. Wu, and Z.-Y. Xian, “Holographic lattice in einstein-maxwell-dilaton gravity,” Journal of High Energy Physics, vol. 2013, no. 11, article 006, 2013. View at Publisher · View at Google Scholar
  80. P. McFadden and K. Skenderis, “Holography for cosmology,” Physical Review D, vol. 81, no. 2, Article ID 021301, 5 pages, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  81. G. 't Hooft, “Dimensional reduction in quantum gravity,” Tech. Rep. THU-93-26, 1993. View at Google Scholar
  82. L. Susskind, “A predictive Yukawa unified SO(10) model: higgs and sparticle masses,” Journal of Mathematical Physics, vol. 36, no. 7, article 139, pp. 6377–6396, 1995. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  83. X. Zhang, “Holographic chaplygin gas model‏,” Physics Letters B, vol. 648, no. 5, pp. 329–332, 2007. View at Google Scholar
  84. M. R. Setare, J. Zhang, and X. Zhang, “Statefinder diagnosis in a non-flat universe and the holographic model of dark energy,” Journal of Cosmology and Astroparticle Physics, vol. 2007, no. 3, article 007, p. 703, 2007. View at Publisher · View at Google Scholar
  85. J. Zhang, X. Zhang, and H. Liu, “Statefinder diagnosis for the interacting model of holographic dark energy,” Physics Letters B, vol. 659, no. 1-2, pp. 26–33, 2008. View at Publisher · View at Google Scholar
  86. C. J. Feng, “Holographic cosmological constant and dark energy,” Physics Letters B, vol. 633, 367 pages, 2008. View at Google Scholar
  87. M. Li, X. D. Li, C. Lin, and Y. Wang, “Holographic gas as dark energy,” Communications in Theoretical Physics, vol. 51, no. 1, pp. 181–186, 2009. View at Publisher · View at Google Scholar
  88. M. Jamil, M. U. Farooq, and M. A. Rashid, “Generalized holographic dark energy model,” European Physical Journal C, vol. 61, no. 3, pp. 471–476, 2009. View at Publisher · View at Google Scholar · View at Scopus
  89. R.-G. Cai, “A dark energy model characterized by the age of the universe,” Physics Letters B, vol. 657, no. 4-5, pp. 228–231, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  90. T. P. Sotiriou, S. Liberati, and V. Faraoni, “Theory of gravitation theories: a no-progress report,” International Journal of Modern Physics, vol. 17, no. 3-4, pp. 399–423, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  91. G. Ruppeiner, “Thermodynamics: a riemannian geometric model,” Physical Review A, vol. 20, no. 4, pp. 1608–1613, 1979. View at Publisher · View at Google Scholar · View at Scopus
  92. H. Quevedo, “Geometrothermodynamics,” Journal of Mathematical Physics, vol. 48, no. 1, Article ID 013506, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  93. J. A. S. Lima and J. S. Alcaniz, “Thermodynamics, spectral distribution and the nature of dark energy,” Physics Letters B, vol. 600, no. 3-4, pp. 191–196, 2004. View at Publisher · View at Google Scholar
  94. W. K. Misner, S. Thorne, and J. A . Wheeler, Gravitation, W. H. Freeman, San Francisco, Calif, USA, 1973. View at MathSciNet
  95. A. Krasinski, H. Quevedo, and R. Sussman, “On the thermodynamical interpretation of perfect fluid solutions of the Einstein equations with no symmetry,” Journal of Mathematical Physics, vol. 38, no. 5, pp. 2602–2610, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  96. D. Lynden-Bell and R. Wood, “The gravo-thermal catastrophe in isothermal spheres and the onset of red-giant structure for stellar systems,” Monthly Notices of the Royal Astronomical Society, vol. 138, no. 4, pp. 495–525, 1968. View at Publisher · View at Google Scholar
  97. D. Lynden-Bell, “Negative specific heat in astronomy, physics and chemistry,” Physica A, vol. 263, no. 1–4, pp. 293–304, 1999. View at Publisher · View at Google Scholar
  98. B. Einarsson, “Conditions for negative specific heat in systems of attracting classical particles,” Physics Letters A, vol. 332, no. 5-6, pp. 335–344, 2004. View at Publisher · View at Google Scholar
  99. M. Chevallier and D. Polarski, “Accelerating universes with scaling dark matter,” International Journal of Modern Physics D, vol. 10, no. 2, pp. 213–223, 2001. View at Publisher · View at Google Scholar · View at Scopus
  100. E. V. Linder, “Exploring the expansion history of the universe,” Physical Review Letters, vol. 90, 4 pages, 2003. View at Publisher · View at Google Scholar
  101. R. G. Cai and S. P. Kim, “First law of thermodynamics and friedmann equations of friedmann-robertson-walker universe,” Journal of High Energy Physics, vol. 0502, article 050, 2005. View at Publisher · View at Google Scholar
  102. R. G. Cai, L. M. Cao, and Y. P. Hu, “Hawking radiation of an apparent horizon in a FRW universe,” Classical and Quantum Gravity, vol. 26, no. 15, Article ID 155018, 2009. View at Publisher · View at Google Scholar
  103. S. del Campo, I. Duran, R. Herrera, and D. Pavon, “Three thermodynamically-based parametrizations of the deceleration parameter,” Physical Review D, vol. 86, Article ID 083509, 2012. View at Publisher · View at Google Scholar
  104. T. Jacobson, “Thermodynamics of spacetime: the Einstein equation of state,” Physical Review Letters, vol. 75, p. 1260, 1995. View at Publisher · View at Google Scholar
  105. C. Rovelli, “General relativistic statistical mechanics,” Physical Review D, vol. 87, no. 8, Article ID 084055, 2013. View at Publisher · View at Google Scholar
  106. J. A. S. Lima, A. I. Silva, and S. M. Viegas, “Is the radiation temperature-redshift relation of the standard cosmology in accordance with the data?” Monthly Notices of the Royal Astronomical Society, vol. 312, no. 4, pp. 747–752, 2000. View at Publisher · View at Google Scholar · View at Scopus
  107. A. Avgoustidis, L. Verde, and R. Jimenez, “Consistency among distance measurements: transparency, BAO scale and accelerated expansion,” Journal of Cosmology and Astroparticle Physics, vol. 2009, no. 6, article 012, p. 906, 2009. View at Publisher · View at Google Scholar
  108. A. Aviles, C. Gruber, O. Luongo, and H. Quevedo, “Cosmography and constraints on the equation of state of the Universe in various parametrizations,” Physical Review D, vol. 86, no. 12, Article ID 123516, 2012. View at Publisher · View at Google Scholar · View at Scopus
  109. C. Gruber and O. Luongo, “Cosmographic analysis of the equation of state of the universe through Padé approximations,” Physical Review D, vol. 89, no. 10, Article ID 103506, 2014. View at Publisher · View at Google Scholar
  110. C. Cattoen and M. Visser, “Cosmography: Extracting the Hubble Series from the Supernova Data,” 2007, https://arxiv.org/abs/gr-qc/0703122.
  111. R.-G. Cai and Z.-L. Tuo, “Detecting the cosmic acceleration with current data,” Physics Letters B, vol. 706, no. 2-3, pp. 116–122, 2011. View at Publisher · View at Google Scholar
  112. A. C. C. Guimaraes and J. A. S. Lima, “Could the cosmic acceleration be transient? A cosmographic evaluation,” Classical and Quantum Gravity, vol. 28, Article ID 125026, 2011. View at Google Scholar
  113. M. Visser, “Cosmography: cosmology without the Einstein equations,” General Relativity and Gravitation, vol. 37, no. 9, pp. 1541–1548, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  114. M. Visser, “Jerk, snap and the cosmological equation of state,” Classical and Quantum Gravity, vol. 21, no. 11, pp. 2603–2615, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  115. A. R. Neben and M. S. Turner, “Beyond H0 and q0: cosmology is no longer just two numbers,” The Astrophysical Journal, vol. 769, no. 2, article 133, 2013. View at Publisher · View at Google Scholar
  116. M. Arabsalmani and V. Sahni, “Statefinder hierarchy: an extended null diagnostic for concordance cosmology,” Physical Review D, vol. 83, Article ID 043501, 2011. View at Publisher · View at Google Scholar