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Class of Exact Solutions for a Cosmological Model of Unified Gravitational and Quintessence Fields

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Abstract

A new approach to tackle Einstein equations for an isotropic and homogeneous Friedmann–Robertson–Walker Universe in the presence of a quintessence scalar field is devised. It provides a way to get a simple exact solution to these equations. This solution determines the quintessence potential uniquely and it differs from solutions which have been used to study inflation previously. It relays on a unification of geometry and dark matter implemented through the definition of a functional relation between the scale factor of the Universe and the quintessence field. For a positive curvature Universe, this solution produces perpetual accelerated expansion rate of the Universe, while the Hubble parameter increases abruptly, attains a maximum value and decreases thereafter. The behavior of this cosmological solution is discussed and its main features are displayed. The formalism is extended to include matter and radiation.

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References

  1. Ryden, B.: Introduction to Cosmology. Addison Wesley, San Francisco (2003)

    Google Scholar 

  2. Tsujikawa, S.: Introductory review of cosmic inflation (2003). arXiv:hep-ph/0304257

  3. Guth, A.: Inflationary universe: a possible solution to the horizon and flatness problems. Phys. Rev. D 23, 347 (1981)

    Article  ADS  Google Scholar 

  4. Liddle, A. R.: An introduction to cosmological inflation (1999). arXiv:astro-ph/9901124

  5. Watson, S.: An Exposition on Inflationary Cosmology (2000). arXiv:astro-ph/0005003

  6. Brandenberger, R.H.: Inflationary cosmology: progress and problems. Astrophys. Space Sci. Libr. 247, 169 (2000)

    Article  Google Scholar 

  7. Linde, A.: Particle Physics and Inflationary Cosmology. Harwood Academic Publishers, Chur (1990)

    Book  Google Scholar 

  8. de la Macorra, A., Piccinelli, G.: Cosmological evolution of general scalar fields and quintessence. Phys. Rev. D 61, 123503 (2000)

    Article  ADS  Google Scholar 

  9. Barreiro, T., Copeland, E.J., Nunes, N.J.: Quintessence arising from exponential potentials. Phys. Rev. D 61, 127301 (2000)

    Article  ADS  Google Scholar 

  10. Rubano, C., Scudellaro, P.: On some exponential potentials for a cosmological scalar field as quintessence. Gen. Relativ. Gravit. 34, 307 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  11. Bartolo, N., Pietroni, M.: Scalar-tensor gravity and quintessence. Phys. Rev. D 61, 023518 (1999)

    Article  ADS  Google Scholar 

  12. Banerjee, N., Pavón, D.: A quintessence scalar field in Brans-Dicke theory. Class. Quantum Gravity 18, 593 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. Matos, T., Ureña-López, L.A.: Quintessence and scalar dark matter in the Universe. Class. Quantum Gravity 17, L75 (2000)

    Article  MATH  Google Scholar 

  14. Matos, T., Siddhartha Guzmán, F., Ureña-López, L.A.: Scalar field as dark matter in the universe. Class. Quantum Gravity 17, 1707 (2000)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. Sahni, V., Wang, L.: New cosmological model of quintessence and dark matter. Phys. Rev. D 62, 103517 (2000)

    Article  ADS  Google Scholar 

  16. Gu, J.-A., Hwang, W.-Y.P.: Can the quintessence be a complex scalar field? Phys. Lett. B 517, 1 (2001)

    Article  ADS  MATH  Google Scholar 

  17. Paliathanasis, A., Tsamparlis, M., Basilakos, S., Barrow, J.D.: Dynamical analysis in scalar field cosmology. Phys. Rev. D 91, 123535 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  18. Ureña-López, L.A., Matos, T.: New cosmological tracker solution for quintessence. Phys. Rev. D 62, 081302 (2000)

    Article  ADS  Google Scholar 

  19. Sahni, V., Starobinsky, A.A.: The case for a positive cosmological \(\Lambda \)-term. Int. J. Mod. Phys. D 9, 373 (2000)

    ADS  Google Scholar 

  20. Chimento, L.P., Jakubi, A.S.: Scalar field cosmologies with perfect fluid in Robertson-Walker metric. Int. J. Mod. Phys. D 5, 71 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  21. Rubano, C., Barrow, J.D.: Scaling solutions and reconstruction of scalar field potentials. Phys. Rev. D 64, 127301 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  22. Russo, J.: Exact solution of scalar field cosmology with exponential potentials and transient acceleration. Phys. Lett. B 600, 185 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Fré, P., Sagnotti, A., Sorin, A.S.: Integrable scalar cosmologies I. Foundations and links with string theory. Nucl. Phys. B 877, 1028 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. Muslimov, A.G.: On the scalar field dynamics in a spatially flat Friedman universe. Class. Quantum Gravity 7, 231 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  25. Ellis, G.F., Madsen, M.S.: Exact scalar field cosmologies. Class. Quantum Gravity 8, 667 (1991)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. Barrow, J.D., Saich, P.: Scalar-field cosmologies. Class. Quantum Gravity 10, 279 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  27. Basilakos, S., Tsamparlis, M., Paliathanasis, A.: Using the Noether symmetry approach to probe the nature of dark energy. Phys. Rev. D 83, 103512 (2011)

    Article  ADS  Google Scholar 

  28. Paliathanasis, A., Tsamparlis, M., Basilakos, S.: Dynamical symmetries and observational constraints in scalar field cosmology. Phys. Rev. D 90, 103524 (2014)

    Article  ADS  Google Scholar 

  29. Kamenshchik, A.Y., Pozdeeva, E.O., Alessandro, T., Venturi, G., Vernov, S.Y.: Interdependence between integrable cosmological models with minimal and non-minimal coupling. Class. Quantum Gravity 33, 015004 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. Kamenshchik, A.Y., Pozdeeva, E.O., Alessandro, T., Venturi, G., Vernov, S.Y.: Integrable cosmological models with non-minimally coupled scalar fields. Class. Quantum Gravity 31, 105003 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  31. Easther, R.: Exact superstring motivated cosmological models. Class. Quantum. Gravity 10, 2203 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  32. Gumjudpai, B.: Scalar field exact solutions for non-flat FLRW cosmology: a technique from non-linear Schrdinger-type formulation. Gen. Relative. Grav. 41, 249 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  33. Steinhardt, P.J.: A quintessential introduction to dark energy. Philos. Trans. R. Soc. Lond. A 361, 2497 (2003)

    Article  ADS  MATH  Google Scholar 

  34. Hojman, S., Rosenbaum, M., Ryan, M.P., Shepley, L.C.: Gauge invariance, minimal coupling, and torsion. Phys. Rev. D 17, 3141 (1978)

    Article  ADS  MathSciNet  Google Scholar 

  35. Tsujikawa, S.: Quintessence: a review. Class. Quantum Gravity 30, 214003 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  36. Copeland, E.J., Sami, M., Tsujikawa, S.: Dynamics of dark energy. Int. J. Mod. Phys. D 15, 1753 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. Capozziello, S., Roshan, M.: Exact cosmological solutions from Hojman conservation quantities. Phys. Lett. B 726, 471 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  38. Chamseddinea, A.H., Mukhanov, V.: Mimetic dark matter. JHEP 11, 135 (2013)

    Article  ADS  Google Scholar 

  39. Salopek, D.S., Bond, J.R.: Nonlinear evolution of long-wavelength metric fluctuations in inflationary models. Phys. Rev. D 42, 3936 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  40. Neupane, I.P.: Accelerating cosmologies from exponential potentials. Class. Quantum Gravity 21, 4383 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  41. Elizalde, E., Nojiri, S., Odintsov, S.D.: Late-time cosmology in a (phantom) scalar-tensor theory: dark energy and the cosmic speed-up. Phys. Rev. D 70, 043539 (2004)

    Article  ADS  Google Scholar 

  42. Bazeia, D., Gomes, C.B., Losano, L., Menezes, R.: First-order formalism and dark energy. Phys. Lett. B 633, 415 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  43. Harko, T., Lobo, F.S.N., Mak, M.K.: Arbitrary scalar-field and quintessence cosmological models. Eur. Phys. J. C 74, 2784 (2014)

    Article  ADS  Google Scholar 

  44. Hojman, S.A., Asenjo, F.A.: Supersymmetric Majorana quantum cosmologies. Phys. Rev. D 92, 083518 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  45. Kamenshchik, A.Y., Manti, S.: Scalar field potentials for closed and open cosmological models. Gen. Relativ. Gravit. 44, 2205 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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Acknowledgements

F.A.A. thanks the CONICyT-Chile for partial support through Funding No. 79130002. S.A.H. expresses his gratitude to Rafael Rosende for his enthusiastic support.

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Authors and Affiliations

  1. Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Santiago, Chile

    Felipe A. Asenjo

  2. Departamento de Ciencias, Facultad de Artes Liberales, Universidad Adolfo Ibáñez, Santiago, Chile

    Sergio A. Hojman

  3. Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago, Chile

    Sergio A. Hojman

  4. Centro de Recursos Educativos Avanzados, CREA, Santiago, Chile

    Sergio A. Hojman

Authors
  1. Felipe A. Asenjo
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  2. Sergio A. Hojman
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Correspondence to Felipe A. Asenjo.

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Asenjo, F.A., Hojman, S.A. Class of Exact Solutions for a Cosmological Model of Unified Gravitational and Quintessence Fields. Found Phys 47, 887–896 (2017). https://doi.org/10.1007/s10701-017-0091-6

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  • DOI: https://doi.org/10.1007/s10701-017-0091-6

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