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A mathematical analysis of the evolution of perturbations in a modified Chaplygin gas model

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Abstract

One approach in modern cosmology consists in supposing that dark matter and dark energy are different manifestations of a single “quartessential” fluid. Following such idea, this work presents a study of the evolution of perturbations of density in a flat cosmological model with a modified Chaplygin gas acting as a single component. Our goal is to obtain properties of the model which can be used to distinguish it from another cosmological models which have the same solutions for the general evolution of the scale factor of the universe, without the construction of the power spectrum. Our analytical results, which alone can be used to uniquely characterize the specific model studied in our work, show that the evolution of the density contrast can be seen, at least in one particular case, as composed by a spheroidal wave function. We also present a numerical analysis which clearly indicates as one interesting feature of the model the appearance of peaks in the evolution of the density contrast.

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References

  1. Perlmutter, S. et al.: Astrophys. J. 517, 565 (1999)

    Article  ADS  Google Scholar 

  2. Riess, A.G. et al.: Astron. J. 116, 1009 (1998)

    Article  ADS  Google Scholar 

  3. Bennett, C.L. et al.: Astrophys. J. Suppl. 148, 1 (2003)

    Article  ADS  Google Scholar 

  4. Turner, M.S.: Sciences 40, 32 (2000)

    ADS  Google Scholar 

  5. Kamenshchik, A., Moschella, U., Pasquier, V.: Phys. Lett. B 511, 265 (2001)

    Article  MATH  ADS  Google Scholar 

  6. Bento, M.C., Bertolami, O., Sen, A.A.: Phys. Rev. D 66, 043507 (2002)

    Article  ADS  Google Scholar 

  7. Bento, M.C., Bertolami, O., Sen, A.A.: Phys. Rev. D 70, 083519 (2004)

    Article  ADS  Google Scholar 

  8. Makler, M., Oliveira, S.Q., Waga, I.: Phys. Lett. B 555, 1 (2003)

    Article  ADS  Google Scholar 

  9. Ananda, K.N., Bruni, M.: Phys. Rev. D 74, 023523 (2006)

    Article  ADS  Google Scholar 

  10. Ananda, K.N., Bruni, M.: Phys. Rev. D 74, 023524 (2006)

    Article  ADS  Google Scholar 

  11. Diez-Tejedor, A., Feinstein, A.: Phys. Rev. D 74, 023530 (2006)

    Article  ADS  Google Scholar 

  12. Giannakis, D., Hu, W.: Phys. Rev. D 72, 063502 (2005)

    Article  ADS  Google Scholar 

  13. Perrota, F., Matarrese, S., Torki, M.: Phys. Rev. D 70, 121304 (2004)

    Article  ADS  Google Scholar 

  14. Gorini, V. et al.: Phys. Rev. D 72, 103518 (2005)

    Article  ADS  Google Scholar 

  15. Carturan, D., Finelli, F.: Phys. Rev. D 68, 103501 (2003)

    Article  ADS  Google Scholar 

  16. Zhu, Z.H.: Astron. Astrophys. 423, 421 (2004)

    Article  MATH  ADS  Google Scholar 

  17. Sandvik, H.B. et al.: Phys. Rev. D 69, 123524 (2004)

    Article  ADS  Google Scholar 

  18. Scherrer, R.J.: Phys. Rev. Lett. 93, 011301 (2004)

    Article  ADS  Google Scholar 

  19. Dev, A., Jain, D., Alcaniz, J.S.: Astron. Astrophys. 417, 847 (2004)

    Article  ADS  Google Scholar 

  20. Avelino, P.P. et al.: Phys. Rev. D 69, 041301 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  21. Amendola, L. et al.: J. Cosmol. Astropart. Phys. 7, 005 (2003)

    Article  ADS  Google Scholar 

  22. Beca, L.M.G. et al.: Phys. Rev. D 67, 101301 (2003)

    Article  ADS  Google Scholar 

  23. Velasquez-Toribio, A.M.: Braz. J. Phys. 36, 772 (2006)

    Article  Google Scholar 

  24. Amendola, L. et al.: Phys. Rev. D 74, 063524 (2006)

    Article  ADS  Google Scholar 

  25. Amendola, L., Waga, I., Finelli, F.: J. Cosmol. Astropart. Phys. 11, 009 (2005)

    Article  ADS  Google Scholar 

  26. Colistete, R., Fabris, J.C.: Class. Quantum Grav. 22, 2813 (2005)

    Article  MATH  ADS  Google Scholar 

  27. Reis, R.R.R., Makler, M., Waga, I.: Class. Quantum Grav. 22, 1191 (2005)

    Article  MATH  ADS  Google Scholar 

  28. Reis, R.R.R., Makler, M., Waga, I.: Class. Quantum Grav. 22, 353 (2005)

    Article  MATH  ADS  Google Scholar 

  29. Reis, R.R.R., Makler, M., Waga, I.: Phys. Rev. D 69, 101301 (2004)

    Article  ADS  Google Scholar 

  30. Avelino, P.P. et al.: Phys. Rev. D 69, 041301 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  31. Makler, M., de Oliveira, S.Q., Waga, I.: Phys. Rev. D 68, 123521 (2003)

    Article  ADS  Google Scholar 

  32. Reis, R.R.R. et al.: Phys. Rev. D 68, 061302 (2003)

    Article  ADS  Google Scholar 

  33. Benaoum, H.B.: hep-th/0205140 (2005)

  34. Debnath, U., Banerjee, A., Chakraborty, S.: Class. Quantum Grav. 21, 5609 (2004)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  35. Chimento, L.P.: Phys. Rev. D 69, 123517 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  36. Barreiro, T., Sen, A.A.: Phys. Rev. D 70, 124013 (2004)

    Article  ADS  Google Scholar 

  37. Costa, S.S., Makler, M.: astro-ph/0702418 (2007)

  38. Costa, S.S.: Braz. J. Phys. 35, 1046 (2005)

    Google Scholar 

  39. Koivisto, T., Mota, D.F.: Phys. Rev. D 73, 083502 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  40. Carneiro, S., Pigozzo, C., Borges, H.A., Alcaniz, J.S.: Phys. Rev. D 74, 023532 (2006)

    Article  ADS  Google Scholar 

  41. Ryden, B.: Introduction to Cosmology. Addison-Wesley, Reading (2003)

    Google Scholar 

  42. Hawking, S.W.: Astrophys. J. 145, 544 (1966)

    Article  ADS  Google Scholar 

  43. Olson, D.W.: Phys. Rev. D 14, 327 (1976)

    Article  ADS  Google Scholar 

  44. Lyth, D.H., Mukherjee, M.: Phys. Rev. D 38, 485 (1988)

    Article  ADS  Google Scholar 

  45. Lyth, D.H., Stewart, E.D.: Astrophys. J. 361, 343 (1990)

    Article  ADS  Google Scholar 

  46. Padmanabhan, T.: Structure Formation in the Universe. Cambridge University Press, Cambridge (1993)

    Google Scholar 

  47. Kolb, E.W., Turner, M.S.: The Early Universe. Addison-Wesley, Reading (1993)

    Google Scholar 

  48. Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series and Products. Academic Press, New York (2000)

    MATH  Google Scholar 

  49. Stratton, J.A.: Proc. Natl. Acad. Sci. 21, 51 (1935)

    Article  MATH  ADS  Google Scholar 

  50. Stratton, J.A.: Proc. Natl. Acad. Sci. 21, 316 (1935)

    Article  MATH  ADS  Google Scholar 

  51. Morse, P.M., Feshbach, H.: Methods of Theoretical Physics. McGraw-Hill, New York (1953)

    MATH  Google Scholar 

  52. Leaver, E.W.: J. Math. Phys. 27, 1238 (1986)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  53. Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York (1972)

    MATH  Google Scholar 

  54. Weisstein, E.W.: Prolate Spheroidal Function, MathWorld—A Wolfram Resource. http://mathworld.wolfram.com/ProlateSpheroidalWaveFunction.html

  55. Carneiro, S.: Modelo cosmológico com decaimento do vácuo—novos resultados e limites observacionais, talk presented at the VI Workshop Nova Fí sica no Espaço (2007)

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Authors and Affiliations

  1. Centro de Ciências Naturais e Humanas, Universidade Federal do ABC, 09210-170, Santo André, São Paulo, Brazil

    Sandro S. e Costa & Maximiliano Ujevic

  2. Departamento de Física, Universidade Federal de Mato Grosso, 78060-900, Cuiabá, Mato Grosso, Brazil

    Alesandro Ferreira dos Santos

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  1. Sandro S. e Costa
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  2. Maximiliano Ujevic
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  3. Alesandro Ferreira dos Santos
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Correspondence to Sandro S. e Costa.

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e Costa, S.S., Ujevic, M. & dos Santos, A.F. A mathematical analysis of the evolution of perturbations in a modified Chaplygin gas model. Gen Relativ Gravit 40, 1683–1703 (2008). https://doi.org/10.1007/s10714-007-0569-1

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  • DOI: https://doi.org/10.1007/s10714-007-0569-1

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