Foundations of Physics

, Volume 46, Issue 4, pp 409–427 | Cite as

Unified Description of Bianchi Type-I Universe in \(f\,(R)\) Gravity

  • S. D. KatoreEmail author
  • S. P. Hatkar
  • R. J. Baxi


The present study explores the Bianchi type I universe in the frame work of f(R) theory of gravity by considering strange quark matter attached to string cloud and domain walls in the presence and absence of magnetism. Field equations are solved by choosing a constant curvature method. It is found that obtained cosmological models are relevant to the early era of evolution of the universe. The strange quark matter may be a source of string cloud and domain walls.


Bianchi type I Strange quark matter String cloud  Domain walls f(R) gravity 



Mrs. R.J.Baxi is grateful to the Department of Science and Technology (DST) New Delhi, India, for providing INSPIRE fellowship (No.IF140404). We are very much thankful to referee for his valuable suggestions and guidelines for the up gradation of the manuscript.


  1. 1.
    Perlmutter, S., et al.: Measurement of \(\Omega \) and \(\Lambda \) from 42 high-redshift supernovae. Astrophys J. 517, 565 (1999)CrossRefADSGoogle Scholar
  2. 2.
    Riess, A.G.: Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116, 1009 (1998)CrossRefADSGoogle Scholar
  3. 3.
    Spergel, D.N., et al.: First year Wilkinson microwave anisotropy probe observational: determination of cosmological parameters. Astrophys. J. Suppl. 148, 175 (2003)CrossRefADSGoogle Scholar
  4. 4.
    Tegmark, M., et al.: Cosmological parameters from SDSS and WMAP. Phys. Rev. D. 69, 103501 (2004)CrossRefADSGoogle Scholar
  5. 5.
    Caldwell, R.R., Dave, R.: Cosmological imprint of an energy component with general equation of state. Phys. Rev. Lett. 82, 1582–1585 (1988)Google Scholar
  6. 6.
    Peebles, P.J.E., Ratra, B.: Cosmological consequences of a rolling homogeneous scalar field. Phys. Rev. D 37, 3406 (1998)Google Scholar
  7. 7.
    Carroll, S.M., DeFelice, A., Duvvuri, V., Easson, V.D.A., Trodden, M., Turner, M.S.: Cosmology of generalized modified gravity models. Phys. Rev. D. 71, 063513 (2005)CrossRefADSGoogle Scholar
  8. 8.
    Shojai, A., Shojai, F.: Some static sherically symmetric interior solutions of \(f(R)\) gravity. Gen. Relat. Grav. 44, 211–223 (2012)CrossRefADSMathSciNetzbMATHGoogle Scholar
  9. 9.
    Fairbain, M., Rydbeck, S.: Expansion History and \(f(R)\) modified gravity. J. Cosm. Astropart. Phys. 5(12), 1–15 (2007)Google Scholar
  10. 10.
    Appleby, S.A., Battye, R.A.: Aspects of cosmological expansion in \(f(R)\) gravity models. J. Assoc. Chest Phys. 05, 019 (2008)Google Scholar
  11. 11.
    Girones, Z., Marchetti, A., Mena, O., Pena-Garay, C., Rius, N.: Cosmological data analysis of \(f(R)\) gravity models. arXiv:0912.5474v1 (2009)
  12. 12.
    Sharif, M., Shamir, M.F.: Non-vacuum Bianchi type I and V in \(f(R)\) gravity. Gen. Relat. Gravit. 42, 2643–2655 (2010)CrossRefADSMathSciNetzbMATHGoogle Scholar
  13. 13.
    Sancheti, M.M., Katore, S.D., Hatkar, S.P.: Anisotropic homogeneous hypersurface with bulk viscosity in \(f(R)\) gravity. Int. J. Math. Sci. Eng. Appl. 7, 391–402 (2013)Google Scholar
  14. 14.
    Vilenkin, A.: Cosmic string and domain walls. Phys. Rep. 121, 263–315 (1985)CrossRefADSMathSciNetzbMATHGoogle Scholar
  15. 15.
    Rajaraman, R.: Solutions & Instantons. North Holland Publishing, Amsterdam (1987)Google Scholar
  16. 16.
    Nielsen, H.B., Olesen, P.: Vortex-line models for dual strings. Nucl. Phys. B 61, 45 (1973)CrossRefADSGoogle Scholar
  17. 17.
    Bachs, C., Tomaras, N.: Higgs-sector solitons. Phys. Rev. D 51, 5356 (1995)CrossRefADSGoogle Scholar
  18. 18.
    Hooft, Gt: A two-dimensional model for mesons. Nucl. Phys. B 75, 276 (1974)CrossRefGoogle Scholar
  19. 19.
    Itoh, N.: Hydrostatic equilibrium of hypothetical quark stars. Prog. Theor. Phys. 44, 291 (1970)CrossRefADSGoogle Scholar
  20. 20.
    Bodmer, A.R.: Collapsed nuclei. Phys. Rev. D. 4, 1601 (1971)CrossRefADSGoogle Scholar
  21. 21.
    Witten, E.: Cosmic separation of phases. Phys. Rev. D. 30, 272 (1984)CrossRefADSGoogle Scholar
  22. 22.
    Kapusta, J.: Finite Temperature Field Theory. Cambridge University Press, Cambridge (1994)Google Scholar
  23. 23.
    Sotani, H., Kohri, K., Harada, T.: Restricting quark matter models by gravitational wave observation. Phys. Rev. D. 69, 084008 (2004)CrossRefADSGoogle Scholar
  24. 24.
    Yilmaz, I.: String cloud and domain walls with quark matter in 5-D Kaluza–Klein cosmological model. Gen. Relat. Grav. 38, 1397–1406 (2006)CrossRefADSMathSciNetzbMATHGoogle Scholar
  25. 25.
    Katore, S.D., Shaikh, A.Y.: Einstein–Rosen string cosmological model in Barber’s second self creasion theory. Int. J. Mod. Phys. A 26, 1651–1657 (2011)CrossRefADSMathSciNetzbMATHGoogle Scholar
  26. 26.
    Katore, S.D., Adhav, K.S., Shaikh, A.Y., Sarkate, N.K.: Higher dimensional LRS Bianchi type-I domain walls in a scalar-tensor theory of gravitation. Int. J. Theor. Phys. 49(10), 2358–2363 (2010)CrossRefMathSciNetzbMATHGoogle Scholar
  27. 27.
    Manhanta, K.L., Biswal, A.K.: String cloud and Domain walls with quark matter in Lyra geometry. J. Mod. Phys. 3, 1479–1486 (2012)CrossRefGoogle Scholar
  28. 28.
    Yilmaz, I., Baysal, H., Aktas, C.: Quark and strange quark matter in \(f(R)\) gravity for Bianchi type I and V space times. Gen. Relat. Gravit. 44, 2313–2328 (2012)CrossRefADSMathSciNetzbMATHGoogle Scholar
  29. 29.
    Letelier, P.S.: String cosmologies. Phys. Rev. D. 28, 2414 (1983)CrossRefADSMathSciNetGoogle Scholar
  30. 30.
    Saha, B., Visinescu, M.: Bianchi type I magnetic string cosmological model. Phys. AUC 18, 46–52 (2008)Google Scholar
  31. 31.
    Thorne, K.S.: Primordial element formation, primordial magnetic fields, and the isotropy of the universe. Astrophys. J. 148, 51–68 (1967)CrossRefADSGoogle Scholar
  32. 32.
    Kantowski, R., Sachs, R.K.: Some spatially homogeneous anisotropic relativistic cosmological models. J. Math. Phys. 7, 433–446 (1966)CrossRefADSMathSciNetGoogle Scholar
  33. 33.
    Kristian, J., Sachs, R.K.: Observations in cosmology. Astrophys. J. 143, 379 (379)Google Scholar
  34. 34.
    Pradhan, A., Kumar, S.S., Jotania, K.: Anisotropic Bianchi type I massive string cosmological models in general relativity. Palestine J. Math. 1(2), 118–132 (2012)Google Scholar
  35. 35.
    Larranaga, A.: A rotating charged black hole solution in \(f(R)\) gravity. Pramana J. Phys. 78, 697–703 (2012)CrossRefADSGoogle Scholar
  36. 36.
    Zel’dovich, YaB: Cosmological fluctuations produced near a singularity. Mon. Not. R. Astron. Soc. 1 192, 663 (1980)CrossRefADSGoogle Scholar
  37. 37.
    Bali, R.: Bianchi type V magnetized string dust universe with variable magnetic permeability. Electron. J. Theor. Phys. 5(9), 105–114 (2008)MathSciNetGoogle Scholar
  38. 38.
    Singh, C.P.: The role of magnetic field in anisotropic string cosmological model. Int. J. Theor. Phys. 53, 1533–1546 (2014)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of MathematicsSant Gadge Baba Amravati UniversityAmravatiIndia
  2. 2.Departments of MathematicsAdarsh Education Societys, Arts, Commerce & Science CollegeHingoliIndia

Personalised recommendations