Does Chaplygin gas have salvation?

  • Juliano P. Campos
  • Júlio C. Fabris
  • Rafael Perez
  • Oliver F. PiattellaEmail author
  • Hermano Velten
Regular Article - Theoretical Physics


We investigate the unification scenario provided by the generalized Chaplygin gas model (a perfect fluid characterized by an equation of state p=−A/ρ α ). Our concerns lie with a possible tension existing between background kinematic tests and those related to the evolution of small perturbations. We analyze data from the observation of the differential age of the universe, type Ia supernovae, baryon acoustic oscillations, and the position of the first peak of the angular spectrum of the cosmic background radiation. We show that these tests favor negative values of the parameter α: we find \(\alpha = - 0.089^{+0.161}_{-0.128}\) at the 2σ level and that α<0 with 85 % confidence. These would correspond to negative values of the square speed of sound which are unacceptable from the point of view of structure formation. We discuss a possible solution to this problem, when the generalized Chaplygin gas is framed in the modified theory of gravity proposed by Rastall. We show that a fluid description within this theory does not serve the purpose, but it is necessary to frame the generalized Chaplygin gas in a scalar field theory. Finally, we address the standard general relativistic unification picture provided by the generalized Chaplygin gas in the case α=0: this is usually considered to be undistinguishable from the standard ΛCDM model, but we show that the evolution of small perturbations, governed by the Mészáros equation, is indeed different and the formation of sub-horizon GCG matter halos may be importantly affected in comparison with the ΛCDM scenario.


Dark Matter Dark Energy Cosmic Microwave Background Baryonic Acoustic Oscillation Background Test 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was supported by CNPq (Brazil). HV acknowledges support from the DFG within the Research Training Group 1620 “Models of Gravity”. We would like to thank Alejandro Aviles and Pedro Avelino for enlightening remarks and suggestions.


  1. 1.
    A.G. Riess et al. (Supernova Search Team Collaboration), Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116, 1009 (1998) ADSCrossRefGoogle Scholar
  2. 2.
    S. Perlmutter et al. (Supernova Cosmology Project Collaboration), Measurements of Ω and Λ from 42 high redshift supernovae. Astrophys. J. 517, 565 (1999) ADSCrossRefGoogle Scholar
  3. 3.
    E. Komatsu et al. (WMAP Collaboration), Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: cosmological interpretation. Astrophys. J. Suppl. Ser. 192, 18 (2011) ADSCrossRefGoogle Scholar
  4. 4.
    R.R. Caldwell, M. Kamionkowski, The physics of cosmic acceleration. Annu. Rev. Nucl. Part. Sci. 59, 397 (2009) ADSCrossRefGoogle Scholar
  5. 5.
    G. Bertone, D. Hooper, J. Silk, Particle dark matter: evidence, candidates and constraints. Phys. Rep. 405, 279 (2005) ADSCrossRefGoogle Scholar
  6. 6.
    T. Padmanabhan, Cosmological constant: the weight of the vacuum. Phys. Rep. 380, 235 (2003) MathSciNetADSzbMATHCrossRefGoogle Scholar
  7. 7.
    A.Y. Kamenshchik, U. Moschella, V. Pasquier, An alternative to quintessence. Phys. Lett. B 511, 265 (2001) ADSzbMATHCrossRefGoogle Scholar
  8. 8.
    R. Jackiw, A Particle field theorist’s lectures on supersymmetric, nonAbelian fluid mechanics and d-branes. physics/0010042
  9. 9.
    M.C. Bento, O. Bertolami, A.A. Sen, Generalized Chaplygin gas, accelerated expansion and dark energy matter unification. Phys. Rev. D 66, 043507 (2002) ADSCrossRefGoogle Scholar
  10. 10.
    N. Bilic, G.B. Tupper, R.D. Viollier, Unification of dark matter and dark energy: the inhomogeneous Chaplygin gas. Phys. Lett. B 535, 17 (2002) ADSzbMATHCrossRefGoogle Scholar
  11. 11.
    H. Sandvik, M. Tegmark, M. Zaldarriaga, I. Waga, The end of unified dark matter? Phys. Rev. D 69, 123524 (2004) ADSCrossRefGoogle Scholar
  12. 12.
    L. Amendola, F. Finelli, C. Burigana, D. Carturan, WMAP and the generalized Chaplygin gas. J. Cosmol. Astropart. Phys. 0307, 005 (2003) ADSCrossRefGoogle Scholar
  13. 13.
    T. Barreiro, O. Bertolami, P. Torres, WMAP5 constraints on the unified model of dark energy and dark matter. Phys. Rev. D 78, 043530 (2008) ADSCrossRefGoogle Scholar
  14. 14.
    V. Gorini, A.Y. Kamenshchik, U. Moschella, O.F. Piattella, A.A. Starobinsky, Gauge-invariant analysis of perturbations in Chaplygin gas unified models of dark matter and dark energy. J. Cosmol. Astropart. Phys. 0802, 016 (2008) ADSCrossRefGoogle Scholar
  15. 15.
    O.F. Piattella, The extreme limit of the generalized Chaplygin gas. J. Cosmol. Astropart. Phys. 1003, 012 (2010) ADSCrossRefGoogle Scholar
  16. 16.
    J.C. Fabris, S.V.B. Gonçalves, H.E.S. Velten, W. Zimdahl, Matter power spectrum for the generalized Chaplygin gas model: the Newtonian approach. Phys. Rev. D 78, 103523 (2008) ADSCrossRefGoogle Scholar
  17. 17.
    J.C. Fabris, H.E.S. Velten, W. Zimdahl, Matter power spectrum for the generalized Chaplygin gas model: the relativistic case. Phys. Rev. D 81, 087303 (2010) ADSCrossRefGoogle Scholar
  18. 18.
    R. Colistete Jr., J.C. Fabris, Bayesian analysis of the (generalized) Chaplygin gas and cosmological constant models using the 157 gold SNe Ia data. Class. Quantum Gravity 22, 2813 (2005) ADSzbMATHCrossRefGoogle Scholar
  19. 19.
    J.C. Fabris, P.L.C. de Oliveira, H.E.S. Velten, Contraints on unified models for dark matter and dark energy using H(z). Eur. Phys. J. C 71, 1773 (2011) ADSCrossRefGoogle Scholar
  20. 20.
    R.R.R. Reis, I. Waga, M.O. Calvao, S.E. Joras, Entropy perturbations in quartessence Chaplygin models. Phys. Rev. D 68, 061302 (2003) ADSCrossRefGoogle Scholar
  21. 21.
    L. Amendola, I. Waga, F. Finelli, Observational constraints on silent quartessence. J. Cosmol. Astropart. Phys. 0511, 009 (2005) ADSCrossRefGoogle Scholar
  22. 22.
    J.C. Fabris, T.C.C. Guio, M. Hamani Daouda, O.F. Piattella, Scalar models for the generalized Chaplygin gas and the structure formation constraints. Gravit. Cosmol. 17, 259 (2011) ADSzbMATHCrossRefGoogle Scholar
  23. 23.
    B.L. Lago, M.O. Calvao, S.E. Joras, R.R.R. Reis, I. Waga, R. Giostri, Type Ia supernova parameter estimation: a comparison of two approaches using current datasets. arXiv:1104.2874 [astro-ph.CO]
  24. 24.
    P. Rastall, Generalization of the Einstein theory. Phys. Rev. D 6, 3357 (1972) MathSciNetADSCrossRefGoogle Scholar
  25. 25.
    C.E.M. Batista, M.H. Daouda, J.C. Fabris, O.F. Piattella, D.C. Rodrigues, Rastall cosmology and the Λ CDM model. Phys. Rev. D 85, 084008 (2012) ADSCrossRefGoogle Scholar
  26. 26.
    J.C. Fabris, M.H. Daouda, O.F. Piattella, Note on the evolution of the gravitational potential in Rastall scalar field theories. Phys. Lett. B 711, 232 (2012) ADSCrossRefGoogle Scholar
  27. 27.
    M.H. Daouda, J.C. Fabris, O.F. Piattella, Scalar models for the unification of the dark sector. AIP Conf. Proc. 1471, 57 (2012) ADSCrossRefGoogle Scholar
  28. 28.
    J.C. Fabris, O.F. Piattella, D.C. Rodrigues, C.E.M. Batista, M.H. Daouda, Rastall cosmology. Int. J. Mod. Phys. Conf. Ser. 18, 67 (2012) CrossRefGoogle Scholar
  29. 29.
    T.P. Sotiriou, V. Faraoni, F(R) theories of gravity. Rev. Mod. Phys. 82, 451 (2010) MathSciNetADSzbMATHCrossRefGoogle Scholar
  30. 30.
    P. Horava, Quantum gravity at a Lifshitz point. Phys. Rev. D 79, 084008 (2009) MathSciNetADSCrossRefGoogle Scholar
  31. 31.
    A. Ali, S. Dutta, E.N. Saridakis, A.A. Sen, Horava–Lifshitz cosmology with generalized Chaplygin gas. Gen. Relativ. Gravit. 44, 657 (2012) MathSciNetADSzbMATHCrossRefGoogle Scholar
  32. 32.
    C.-G. Park, J.-c. Hwang, J. Park, H. Noh, Observational constraints on a unified dark matter and dark energy model based on generalized Chaplygin gas. Phys. Rev. D 81, 063532 (2010) ADSCrossRefGoogle Scholar
  33. 33.
    J.C. Fabris, S.V.B. Goncalves, R. de Sa Ribeiro, Generalized Chaplygin gas with α=0 and the ΛCDM cosmological model. Gen. Relativ. Gravit. 36, 211 (2004) ADSzbMATHCrossRefGoogle Scholar
  34. 34.
    P.P. Avelino, L.M.G. Beca, J.P.M. de Carvalho, C.J.A.P. Martins, The ΛCDM limit of the generalized Chaplygin gas scenario. J. Cosmol. Astropart. Phys. 0309, 002 (2003) ADSCrossRefGoogle Scholar
  35. 35.
    J. Simon, L. Verde, R. Jimenez, Constraints on the redshift dependence of the dark energy potential. Phys. Rev. D 71, 123001 (2005) ADSCrossRefGoogle Scholar
  36. 36.
    D. Stern, R. Jimenez, L. Verde, M. Kamionkowski, S.A. Stanford, Cosmic chronometers: constraining the equation of state of dark energy. I: H(z) measurements. J. Cosmol. Astropart. Phys. 1002, 008 (2010) ADSCrossRefGoogle Scholar
  37. 37.
    R. Jimenez, L. Verde, T. Treu, D. Stern, Constraints on the equation of state of dark energy and the Hubble constant from stellar ages and the CMB. Astrophys. J. 593, 622 (2003) ADSCrossRefGoogle Scholar
  38. 38.
    T.-J. Zhang, C. Ma, Constraints on the dark side of the universe and observational Hubble parameter data. Adv. Astron. 2010, 184284 (2010) ADSCrossRefGoogle Scholar
  39. 39.
    C. Ma, T.-J. Zhang, Power of observational Hubble parameter data: a figure of merit exploration. Astrophys. J. 730, 74 (2011) ADSCrossRefGoogle Scholar
  40. 40.
    M. Moresco, A. Cimatti, R. Jimenez, L. Pozzetti, G. Zamorani, M. Bolzonella, J. Dunlop, F. Lamareille et al., Improved constraints on the expansion rate of the universe up to z∼1.1 from the spectroscopic evolution of cosmic chronometers. J. Cosmol. Astropart. Phys. 1208, 006 (2012) ADSCrossRefGoogle Scholar
  41. 41.
    O. Farooq, D. Mania, B. Ratra, Hubble parameter measurement constraints on dark energy. arXiv:1211.4253 [astro-ph.CO]
  42. 42.
    R. Amanullah, C. Lidman, D. Rubin, G. Aldering, P. Astier, K. Barbary, M.S. Burns, A. Conley et al., Spectra and light curves of six type Ia supernovae at 0.511<z<1.12 and the Union2 compilation. Astrophys. J. 716, 712 (2010) ADSCrossRefGoogle Scholar
  43. 43.
    M. Doran, M.J. Lilley, J. Schwindt, C. Wetterich, Quintessence and the separation of CMB peaks. Astrophys. J. 559, 501 (2001) ADSCrossRefGoogle Scholar
  44. 44.
    W. Hu, M. Fukugita, M. Zaldarriaga, M. Tegmark, CMB observables and their cosmological implications. Astrophys. J. 549, 669 (2001) ADSCrossRefGoogle Scholar
  45. 45.
    M. Doran, M. Lilley, C. Wetterich, Constraining quintessence with the new CMB data. Phys. Lett. B 528, 175 (2002) ADSCrossRefGoogle Scholar
  46. 46.
    E.D. Reese, J.E. Carlstrom, M. Joy, J.J. Mohr, L. Grego, W.L. Holzapfel, Determining the cosmic distance scale from interferometric measurements of the Sunyaev–Zel’dovich effect. Astrophys. J. 581, 53 (2002) ADSCrossRefGoogle Scholar
  47. 47.
    J. Lu, L. Xu, Y. Wu, M. Liu, Combined constraints on modified Chaplygin gas model from cosmological observed data: Markov chain Monte Carlo approach. Gen. Relativ. Gravit. 43, 819 (2011) ADSzbMATHCrossRefGoogle Scholar
  48. 48.
    D.J. Eisenstein et al. (SDSS Collaboration), Detection of the baryon acoustic peak in the large-scale correlation function of SDSS luminous red galaxies. Astrophys. J. 633, 560 (2005) ADSCrossRefGoogle Scholar
  49. 49.
    C. Blake et al., The WiggleZ dark energy survey: mapping the distance-redshift relation with baryon acoustic oscillations. Mon. Not. R. Astron. Soc. 418, 3, 1707 (2011) ADSCrossRefGoogle Scholar
  50. 50.
    H. Velten, D.J. Schwarz, Constraints on dissipative unified dark matter. J. Cosmol. Astropart. Phys. 1109, 016 (2011) ADSCrossRefGoogle Scholar
  51. 51.
    R.A.A. Fernandes, J.P.M. de Carvalho, A.Y. Kamenshchik, U. Moschella, A. da Silva, Spherical ‘Top-hat’ collapse in general Chaplygin gas dominated universes. Phys. Rev. D 85, 083501 (2012) ADSCrossRefGoogle Scholar
  52. 52.
    P. Meszaros, The behaviour of point masses in an expanding cosmological substratum. Astron. Astrophys. 37, 225 (1974) ADSGoogle Scholar
  53. 53.
    C. Gao, M. Kunz, A.R. Liddle, D. Parkinson, Unified dark energy and dark matter from a scalar field different from quintessence. Phys. Rev. D 81, 043520 (2010) ADSCrossRefGoogle Scholar
  54. 54.
    P.P. Avelino, L.M.G. Beca, C.J.A.P. Martins, Linear and nonlinear instabilities in unified dark energy models. Phys. Rev. D 77, 063515 (2008) ADSCrossRefGoogle Scholar
  55. 55.
    P.P. Avelino, L.M.G. Beca, C.J.A.P. Martins, Clustering properties of dynamical dark energy models. Phys. Rev. D 77, 101302 (2008) ADSCrossRefGoogle Scholar
  56. 56.
    A. Aviles, J.L. Cervantes-Cota, The dark degeneracy and interacting cosmic components. Phys. Rev. D 84, 083515 (2011). Erratum-ibid. D 84, 089905 (2011) ADSCrossRefGoogle Scholar
  57. 57.
    A. Lewis, A. Challinor, A. Lasenby, Efficient computation of CMB anisotropies in closed FRW models. Astrophys. J. 538, 473 (2000) ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  • Juliano P. Campos
    • 1
  • Júlio C. Fabris
    • 2
  • Rafael Perez
    • 2
  • Oliver F. Piattella
    • 2
    Email author
  • Hermano Velten
    • 3
  1. 1.Centro de Ciências Exatas e TecnológicasUFRBCruz das AlmasBrazil
  2. 2.Departamento de FísicaCCE, UFESVitóriaBrazil
  3. 3.Fakultät für PhysikUniversität BielefeldBielefeldGermany

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