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Dark Energy Scenario in Metric f(R) Formalism

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Abstract

Friedmann–Robertson–Walker (FRW) space–time with bulk viscosity in the context of f(R) gravity is considered. The field equations are solved for the Power and Exponential volumetric expansion. Two types of functional relationship i.e. f(R) = R + bRm and \( \,f(R) = R - \frac{{\lambda^{4} }}{R} \) are investigated. The Phantom, Chaplygin gas and Tachyon fields are discussed. It is observed that the universe is open and inflationary.

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References

  1. Riess, A.G., et al.: Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116, 1009–1038 (1998)

    ADS  Google Scholar 

  2. Perlmutter, S.J., et al.: Measurements of Ω and Λ from 42 high redshift supernovae. Astron. J. 517, 565 (1999)

    MATH  Google Scholar 

  3. Carroll, S.M.: The cosmological constant. Living Rev. Relativ. 4, 1 (2001)

    ADS  MathSciNet  MATH  Google Scholar 

  4. Caldwell, R.R., Dave, R., Steinhardt, P.J.: Cosmological imprint of an energy component with general equation of state. Phys. Rev. Lett. 8, 1582 (1998)

    ADS  MATH  Google Scholar 

  5. Caldwell, R.R.: A phantom menace? Cosmological consequences of dark energy components with super-negative equation of state. Phys. Lett. B 545, 23 (2002)

    ADS  Google Scholar 

  6. Bilic, N., Tupper, G.B., Viollier, R.D.: Unification of dark matter and dark energy: the inhomogeneous chapygin gas. Phys. Lett. B 535, 17 (2002)

    ADS  MATH  Google Scholar 

  7. Wu, Y.B., Li, S., Fu, M.H., He, J.: A modified Chaplygin gas model with interaction. Gen. Relativ. Gravit. 39, 653–662 (2007)

    ADS  MathSciNet  MATH  Google Scholar 

  8. Singh, C.P., Beesham, A.: Hypersurface homogeneous space time with anisotropic dark energy. Gravit. Cosmol. 17(3), 284–290 (2011)

    ADS  MathSciNet  MATH  Google Scholar 

  9. Katore, S.D., Sancheti, M.M., Hatkar, S.P., Sarkate, N.K.: Hypersurface homogeneous space time with anisotropic dark energy in Brans-Dicke theory of gravitation. Commun. Theor. Phys. 62, 768–774 (2014)

    MathSciNet  MATH  Google Scholar 

  10. Zimdhal, W., Pavon, D.: State finder parameters for interacting dark energy. Gen. Reltiv. Gravit. 36, 6 (2004)

    Google Scholar 

  11. Chakraborty, S., Debnath, U.: Energent scenario in anisotropic universe. Int. J. Theor. Phys. 50, 80–87 (2011)

    MATH  Google Scholar 

  12. Katore, S.D., Haktar, S.P.: Kaluza-Klein universe with a magnetized anisotropic dark energy in general relativity and Lyra manifold. New Astron. 34, 172–177 (2015)

    ADS  Google Scholar 

  13. Sahni, V., Shtanov, Y.: Brane world models of dark energy. JCAP 0311, 014 (2003)

    ADS  Google Scholar 

  14. Sahni, V.: Dark matter and dark energy. Lect. Notes Phys. 653, 141–180 (2004)

    ADS  MATH  Google Scholar 

  15. Bamba, K., Geng, C.Q., Nojiri, S., Odintsov, S.D.: Crossing of the Phantom divide in modified gravity. Phys. Rev. D 79, 0803014 (2009)

    MathSciNet  Google Scholar 

  16. Setare, M.R.: Holographic modified gravity. Int. J. Mod. Phys. D 17, 2219 (2008)

    ADS  MathSciNet  MATH  Google Scholar 

  17. Setare, M.R., Jamil, M.: State finder diagnostic and stability of modified gravity consistent with holographic and agegraphic dark energy. Gen. Relativ. Gravit. 43, 293–303 (2011)

    ADS  MATH  Google Scholar 

  18. Katore, S.D., Hatkar, S.P.: Two fluid cosmological models in f(R) theory of gravitation. Indian J. Phys. 90(2), 243–252 (2016)

    ADS  MATH  Google Scholar 

  19. Sharif, M., Sharif, M.F.: Exact solution of Bianchi type I and V space times in the f(R) theory of gravity. Class. Quant. Gravit. 26, 235020 (2009)

    ADS  MATH  Google Scholar 

  20. Guarnizo, A., Castaneda, L., Tejeiro, J.M.: Boundary term in metric f(R) gravity: field equations in the metric formalism. Gen. Relativ. Gravit. 43, 2413–2428 (2011)

    MATH  Google Scholar 

  21. Nzioki, A.M., Carloni, S., Goswami, R., Dunsby, P.K.S.: New framework for studing spherically symmetric static solutions in f(R) gravity. Phys. Rev. D 81(8), 084028 (2010)

    ADS  Google Scholar 

  22. Katore, S.D., Hatkar, S.P., Baxi, R.J.: Unified description of Bianchi type I universe in f(R) gravity. Found. Phys. 46(4), 409–427 (2016)

    ADS  MathSciNet  MATH  Google Scholar 

  23. Bamba, K., Capozziello, S., Nojiri, S., Odintsov, S.D.: Dark energy cosmology: the equivalent description via different theoretical models and cosmolography tests. Astrophys. Space Sci. 342, 155–228 (2012)

    ADS  MATH  Google Scholar 

  24. Capozziello, S., De Laurentis, M.: Extendend theories of gravity. Phys. Rep. 509, 167 (2017)

    ADS  Google Scholar 

  25. Nojiri, S., Odintsov, S.D., Oikonomou, V.K.: Modified gravity theories on a nutshell: inflation, bounce and late-time evolution. Phys. Rep. 692, 1–104 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

  26. Capozziello, S., Francaviglia, M.: Extended theories of gravity and their cosmological and astrophysical applications. Gen. Relativ. Gravit. 40(2–3), 357–420 (2008)

    ADS  MathSciNet  MATH  Google Scholar 

  27. Eckart, C.: The thermodynamics of irreversible processes, III relativistic theory of the simple fluid. Phys. Rev. D 58, 919 (1940)

    ADS  MATH  Google Scholar 

  28. Muller, I.: Zum paradoxonder warmeleitungstheorie. Z. Phys. 198, 329 (1967)

    ADS  MATH  Google Scholar 

  29. Singh, C.P.: Bulk viscous cosmology in early universe. Pramana J. Phys. 71(1), 33–48 (2008)

    ADS  Google Scholar 

  30. Kandalkar, S.P., Khade, P.P., Gawande, S.P.: Bianchi type VI bulk viscous string cosmological model in general relativity. Bulg. J. Phys. 38, 145–154 (2011)

    MathSciNet  Google Scholar 

  31. Singh, M.K., Verma, M.K., Ram, S.: Anisotropic Bianchi type II viscous fluid models with time dependent gravitation and cosmological constant. Int. J. Phys. 1(4), 77–83 (2013)

    Google Scholar 

  32. Misner, C.W.: The isotropy of the universe. Astrophys. J. 151, 431–457 (1968)

    ADS  Google Scholar 

  33. Heller, M., Klimek, Z.: Viscous universes without initial singularity. Astrophys. Space Sci. 33(2), 37 (1975)

    ADS  Google Scholar 

  34. Collins, C.B., Stewart, J.M.: Qualitative cosmology. Mon. Not. R. Astron. Soc. 153, 419 (1971)

    ADS  Google Scholar 

  35. Weinberg, S.: Entropy generation and the survival of protogalaxies in an expanding universe. Astrophys. J. 168, 175 (1971)

    ADS  Google Scholar 

  36. Bali, R., Yadav, M.K.: Bianchi type IX viscous fluid cosmological model in general relativity. Pramana J. Phys. 64(2), 187–196 (2005)

    ADS  Google Scholar 

  37. Barrow, J.D.: Exactly inflationary universe with potential minima. Phys. Rev. D 49, 3055 (1994)

    ADS  MathSciNet  Google Scholar 

  38. Olive, K.A.: Inflation. Phys. Rev. 190, 307 (1990)

    Google Scholar 

  39. Bertolami, O.: Time dependent cosmological constant. Nuovo Cemento Soc. Ital. Fis 93B, 36 (1986)

    ADS  Google Scholar 

  40. Ratra, B., Peebles, P.J.E.: Cosmological consequences of a rolling homogeneous scalar field. Phys. Rev. D 37, 3406 (1988)

    ADS  Google Scholar 

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

    ADS  MATH  Google Scholar 

  42. Coley, A.A., Ibanez, J., Van den Hoogen, R.J.: Homogeneous scalar field cosmologies with an exponential potential. J. Math. Phys. 38, 5256 (1997)

    ADS  MathSciNet  MATH  Google Scholar 

  43. Motavali, M., Capozziello, S., Jog, M.R.A.: Scalar-tensor cosmology with R-1 curvature correction by Noether symmetry. Phys. Lett. B 666, 10 (2008)

    ADS  MathSciNet  MATH  Google Scholar 

  44. Roshan, M., Shojai, F.: Palatini f(R) gravity and Noether symmetry. Phys. Lett. B 668, 238 (2008)

    ADS  MathSciNet  Google Scholar 

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

    ADS  MathSciNet  MATH  Google Scholar 

  46. Nojiri, S., Odintsov, S.D.: Unified cosmic history in modified gravity: from f(R) theory to Lorentz non invariant models. Phys. Rep. 505, 59 (2011)

    ADS  MathSciNet  Google Scholar 

  47. Nojiri, S., Odintsov, S.D.: Introduction to modified gravity and gravitational alternative for dark energy. Int. J. Geom. Methods Mod. Phys. 4, 115 (2007)

    MathSciNet  MATH  Google Scholar 

  48. Ren, J., Meng, X.: Cosmological model with viscosity media (dark fluid) described by an effective equation of state. Phys. Lett. B 633, 1–8 (2006)

    ADS  MATH  Google Scholar 

  49. Capozziello, S., Mantica, C.A., Molinri, L.G.: Cosmological perfect fluids in f(R) gravity. Int. J. Geom. Methods Mod. Phys. 8, 1–39 (2018)

    Google Scholar 

  50. Capozziello, S.: Curvature quintessence. Int. J. Mod. Phys. D 11(4), 483 (2002)

    ADS  MathSciNet  MATH  Google Scholar 

  51. Chaubey, R.: Role of modified Chaplygin gas in Bianchi type I universe. Int. J. Theor. Phys. 48, 952–960 (2009)

    MathSciNet  MATH  Google Scholar 

  52. Olmo, G.J., Alepuz, H.S.: Hamiltonian formulation of palatine f(R) theories a la Brans-Dicke theory. Phys. Rev. D 83, 104036 (2011)

    ADS  Google Scholar 

  53. Starobinsky, A.A.: A new type of isotropic cosmological models with singularity. Phys. Lett. B 91, 99–102 (1980)

    ADS  MATH  Google Scholar 

  54. DeFelice, A., Tsujikawa, S.: f(R) theories. Living Rev. Rel. 13, 3 (2010)

    Google Scholar 

  55. Capozziello, S., De Laurents, M., Stabile, A.: Axially symmetric solutions in f(R) gravity. Class. Quant. Gravit. 27, 165008 (2010)

    ADS  MathSciNet  MATH  Google Scholar 

  56. Ogawa, N.: Remark on the classical solution of the Chaplygin gas as d-branes. Phys. Rev. D 62, 085023 (2000)

    ADS  Google Scholar 

  57. Dolgov, A.D., Kawasaki, M.: Can modified gravity explain accelerated cosmic expansion? Phys. Lett. B 513, 1 (2003)

    ADS  MATH  Google Scholar 

  58. Capozziello, S., Cardone, V.F., Troisi, A.: Reconciling dark energy models with f(R) theories. Phys. Rev. D 71, 043503 (2005)

    ADS  Google Scholar 

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Acknowledgements

The authors would like to thank the anonymous referees for giving very enlightening and constructive suggestions which helped in improving the manuscript.

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Hatkar, S.P., Dudhe, P.S. & Katore, S.D. Dark Energy Scenario in Metric f(R) Formalism. Found Phys 49, 1067–1085 (2019). https://doi.org/10.1007/s10701-019-00302-x

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