6th International Young Scientist Congress (IYSC-2020) will be Postponed to 8th and 9th May 2021 Due to COVID-19. 10th International Science Congress (ISC-2020).  International E-publication: Publish Projects, Dissertation, Theses, Books, Souvenir, Conference Proceeding with ISBN.  International E-Bulletin: Information/News regarding: Academics and Research

Bianchi Type-IX Dark Energy Model in Barber′s Second Self-Creation Theory

Author Affiliations

  • 1Department of Mathematics, Jijamata Mahavidyalaya, Buldana, INDIA

Res. J. Recent Sci., Volume 3, Issue (ISC-2013), Pages 79-85, (2014)


A Bianchi type-IX dark energy cosmological model with variable equation of state (EoS) parameter is obtained in Barber’s second Self-Creation theory of gravitation. The field equations have been solved by applying variation law for generalized Hubble’s parameter given by Bermann. Some physical properties of the models are also discussed.


  1. Perlmutter S. et al., Measurement of and 42 high-Redshift Supernovae, The Astrophys. J., 517(2), 565-586 (1999), 79-85 (2014)
  2. Riess A. G.et al., Type Ia Supernova Discoveries at z ?1 from the Hubble Space Telescope: Evidence for the Past Deceleration and Constraints on Dark Energy Evolution, The Astrophys. J., 607(2), 665-678 (2004)
  3. Spergel D.N. et al., Three-YearWilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for cosmology, Astrophys. J. Suppl. Ser., 170(2), 377 (2007)
  4. Wood-Vaseyet al., Observational constraints on the nature of Dark Energy: first cosmological results from the ESSENCE supernova survey, The Astrophys. J., 666(2),694–715 (2007)
  5. Benett C.L. et al., First-YearWilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results, Astrophys. J. Suppl. Ser., 148(1),1, (2003)
  6. Spergel D.N. et al., First-YearWilkinson Microwave Anisotropy Probe (WMAP) Observations: Determinations of cosmological parameters, Astrophys. J. Suppl. Ser., 148(1), 175, (2003)
  7. Hawkins E. et al., The 2dF galaxy redshift survey: correlation functions, peculiar velocities and the matter density of the universe, Mon. Notices of the Royal Astrono. Soc., 346(1), 78–96 (2003)
  8. Abazajian K. et al., The First Data Release of the Sloan Digital Sky Survey, Astronom. J.,126, 2081 (2003)
  9. Abazajian K. et al., The Second Data Release of the Sloan Digital Sky Survey, Astronom. J., 128, 502 (2004a)
  10. Abazajian K. et al., Cosmological parameters from SDSS and WMAP, Phy. Rev. D, 69, 103501 (2004b)
  11. Tegmark M. et al., Cosmological parameters from SDSS and WMAP, Phys. Rev. D, 69(10) 103501 (2004)
  12. Singh T. and Chaubey R., Bianchi type-V cosmological models with perfect fluid and dark energy, Astrophy. and Spa. Sci., 319, 149-154 (2009)
  13. Akarsu O. and Kilinc C.B., Bianchi Type-III Models with Anisotropic Dark Energy, Gen. Rel. Grav.,42(4), 763-775 (2010)
  14. Adhav K.S., LRS Bianchi Type-I Universe with Anisotropic Dark Energy In Lyra Geometry, Inter. J. Astrono. And Astrophy., 1, 204-209 (2011)
  15. Katore S.D. and Shaikh A.Y., Kantowaski-Sachs Dark Energy model in f(R, T) gravity, Prespacetime J., 3(11),1087-1096 (2012)
  16. Naidu R.L., Satyanarayanrao B. and Reddy D.R.K., Bianchi Type-III Dark Energy model in Saez-Ballester Scalar-Tensor Theory, Int. J. Theo. Phy., 51, 2857-2862 (2012)
  17. Ghate H.R., Sontakke A.S., Bianchi Type-IX Universe with Magnetized Anisotropic Dark Energy, ARPN J. Sci. and Tech., 3(7), 731-742 (2013)
  18. Ghate H.R., Sontakke A.S., Bianchi Type-IX Universe with Anisotropic Dark Energy in Lyra Geometry, Prespacetime J., 4(6), 619–628 (2013)
  19. Ghate H.R. and Sontakke A.S., Bianchi Type-IX Dark Energy Model in Brans-Dicke Theory of Gravitation, Prespacetime J., 4(4), 366–376 (2013)
  20. Brans C.H. and Dicke R.H., Machs Principle and a Relativistic Theory of Gravitation, Phy. Rev., 124, 925-935 (1961)
  21. Nordtvedt K. Jr., Post-Newtonian metric for a general class of scalar-tensor gravitational theories and observational consequences, Astrophy. J., 161(9), 1059-1067 (1970)
  22. Sen D.K., A static cosmological models, Z. Fur Phys., 149,311-323 (1957)
  23. Sen D.K. and Dunn K.A., A scalar-tensor theory of gravitation in a modified Riemannian manifold, J. Math. Phys., 12(4), 578-586 (1971)
  24. Wagoner R.T., Scalar-Tensor theory and gravitational waves, Phys. Rev. D, 1(12), 3209-3216 (1970)
  25. Saez D. and Ballester V.J., A simple coupling with cosmological implications, Phys. Lett. A, 113(9), 467-470 (1985)
  26. Barber G.A., On two Self-Creation Cosmology, Gen. Rel. Grav., 14, 117-136 (1982)
  27. Brans C.H., Consistency of field equations in Self-Creation cosmologies, Gen. Rel. Grav., 19(9), 949-952 (1987)
  28. Pimentel L.O., Exact self-creation cosmological solutions, Astrophysics and Spa. Sci.,116, 395-399 (1985)
  29. Soleng H.H., Self- Creation Cosmological Solutions, Astrophy. Spa. Sci., 139, 13-19 (1987)
  30. Singh T. and Singh T., Some general results in selfcreation cosmologies, Astrophy. Spa. Sci.,102, 67-70 (1984)
  31. Reddy D.R.K., Bianchi type-I Universe filled with disordered radiation in self-creation cosmology, Astrophy. Spa. Sci,133, 389-392 (1987)
  32. Reddy D.R.K., Avadhanulu M.D. and Venkateshwarlu R., Birkhoff-type theorem forelectromagnetic fields in self-creation cosmology, Astrophy. Spa. Sci., 134, 201-204 (1987)
  33. Reddy D.R.K. and Venkateshwarlu R, An anisotropic cosmological model in self-creation cosmology, Astrophy. Spa. Sci., 152, 337-341 (1989) , 79-85 (2014)
  34. Shanthi K. and Rao V.U.M., Bianchi Type –II and III Models in Self Creation Cosmology, Astrophy. Spa. Sci., 179, 147-153 (1991)
  35. Shri Ram and Singh C.P., Anisotropic Bianchi Type II Cosmological Models in Self-Creation Cosmology, Astrophy. Spa. Sci.,257, 287 (1998b)
  36. Pradhan A. and Pandey H.R., Bulk Viscous Cosmological Models in Barber’s Second Self Creation Theory, Int. J. Mod. Phy.; arxiv : gr-qc/0207027v1, (2002)
  37. Pradhan A. and Vishwakarma A.K., LRS Bianchi Type-I Cosmological Models in Barber's Second Self Creation Theory, Int. J. Mod. Phy., D., 11, 1195 (2002)
  38. Panigrahi U.K. and Sahu R.C., Plane symmetric cosmological macro models in self-creation theory of gravitation, Czechoslovak Journal of Physics, 54(5), 543-551 (2004)
  39. Venkateshwarlu R. and Kumar P.K., Higher Dimensional FRW Cosmological Models in Self-Creation Theory, Astrophy.Spa.Sci, 301,73-77 (2006)
  40. Singh C.P. and Kumar S., Bianchi type II space times with constant deceleration parameter in self-creation cosmology, Astrophys. Spa. Sci., 310(1-2), 31-39 (2007)
  41. Venkateswarlu K., Rao V.U.M. and Kumar K.P., String cosmological solutions in self-creation theory of gravitation, Int.J.Theor.Phys., 47(3), 640-648 (2008)
  42. Reddy D.R.K. and Naidu R.L., Kaluza-Klein cosmological models in self-creatiion cosmology, Int. J. Theor. Phys., 48(1), 10-13 (2009)
  43. Katore S.D., Rane R.S. and Wankhade K.S., FRW cosmological models with bulk-viscosity in Barber’s second self-creation theory, Int. J. Theor. Phys., 49(1),187-193 (2010)
  44. Katore S.D., Rane R.S., Wankhade K.S. and Bhaskar S.A., Accelerating and decelerating hypersurface and homogeneous cosmological models in Barber’s second self-creation theory, Global J. Sci. Front. Res.(F), 12(3),(2012)
  45. Mahanta K.L. and Biswal A.K., A dark energy model with variable EoS parameter in Self-Creation theory of gravitation, Rom. Journ. Phys., 58(3-4), 239-246 (2013)
  46. Chakraborty S., A study on Bianchi-IX cosmological model, Astrophy. Spa.Sci., 180(2), 293–303 (1991)
  47. Bali R. and Dave S., Bianchi Type-IX string cosmological model in general relativity, Pramana J. Phy., 56(4), 513–518 (2001)
  48. Bali R. and Yadav M.K., Bianchi Type-IX viscous fluid cosmological model in general relativity, Pramana J. Phy., 64(2), 187–196 (2005)
  49. Pradhan A., Srivastav S.K. and Yadav M.K., Some homogeneous Bianchi type IX viscous fluid cosmological models with a varying , Astrophy. Spa. Sci., 298, 419-432 (2005)
  50. Tyagi A. and Chhajed D., Homogeneous anisotropic Bianchi type-IX cosmological model for perfect fluid distribution with electromagnetic field, American J. Math. And Statis., 2(3), 19-21 (2012)
  51. Ghate H.R. and Sontakke A.S., Bianchi type-IX cosmological models with a anisotropic dark energy, Int.J. Sci. Eng. Res., 4(6), 769-774 (2013)
  52. Ghate H.R. and Sontakke A.S., Binary mixture of Anisotropic dark energy and Perfect fluid in Bianchi Type-IX space-time, JPMS, 3(2), 122-131 (2013)
  53. Thorne K.S., Primordial Element Formation, Primordial Magnetic Fields, and the Isotropy of the Universe, Astrophys. J., 148, 51, (1967)
  54. Kantowski R., Sachs R.K., Some spatially homogeneous anisotropic relativistic cosmological models, Journal of Mathematical Physics, 7(3), 443 (1966)
  55. Kristian J. and Sachs R.K., Observations in Cosmology, Astrophysical journal, 143, 379 (1966)
  56. Collins C.B., Glass E.N. and Wilkinson D.A., Exact spatially homogeneous cosmologies, Gen. Relat. Grav., 12(10), 805-823 (1980)
  57. Bermann M.S., A special law of variation for Hubble’s parameter, Nuovo Cimento B, 74(2), 182–186 (1983)