Skip to main content
Log in

Bianchi Type VI 0 Viscous Fluid Cosmological Models with Time-Dependent Cosmological Term \(\varLambda \)

  • Research Article
  • Published:
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Aims and scope Submit manuscript

Abstract

Bianchi type \({VI}_0\) viscous fluid cosmological models satisfying barotropic equation of state with varying cosmological term \(\varLambda \) are investigated. We have examined a cosmological scenario proposing a constant ratio between shear \(\sigma \) and volume expansion \(\theta \) in the background of homogeneous, anisotropic Bianchi type \({VI}_0\) space–time. The cosmological term \(\varLambda \) is found to be decreasing function of time which is supported by results from recent supernovae Ia observations. The model remains anisotropic throughout the evolution. Cosmological consequences of these models have been discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Weinberg S (1989) The cosmological constant problem. Rev Mod Phys 61:1–24

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Garnavich PM, Kirshner RP, Challis P, Tonry J, Gilliland RL, Smith RC, Clocchiatti A, Dierck A, Filippenko AV, Hamuy M, Hogan J, Leibundgut B, Phillips MM, Reiss D, Riess AG, Schmidt BP, Schommer RA, Spyromilio J, Stubbs C, Suntzeff NB, Wells L (1998) Constraints on cosmological models from Hubble space telescope observations of high-z supernovae. Astrophys J Lett 493:53–57

    Article  ADS  Google Scholar 

  3. Garnavich PM, Jha S, Challis P, Clocchiatti A, Diercks A, Filippenko AV, Gilliland RL, Hogan CJ, Kirshner RP, Leibundgut B, Phillips MM, Reiss D, Riess AG, Schmidt BP, Schommer RA, Smith RC, Spyromilio J, Stubbs C, Suntzeff NB, Tonry J, Carroll SM (1998) Supernova limits on the cosmic equation of state. Astrophys J 509:74–79

    Article  ADS  Google Scholar 

  4. Perlmutter S, Gabi S, Goldhaber G, Goobar A, Groom DE, Hook IM, Kim AG, Kim MY, Lee JC, Pain R, Pennypacker CR, Small IA, Ellis RS, McMahon RG, Boyle BJ, Bunclark PS, Carter D, Irwin MJ, Glazebrook K, Newberg HJM, Filippenko AV, Matheson T, Dopita M, Couch WJ (1997) Measurements of the cosmological parameters \(\Omega \) and \(\Lambda \) from the first seven supernovae at z \(\ge \) 0.35. Astrophys J 483:565–581

    Article  ADS  Google Scholar 

  5. Perlmutter S, Aldering G, Valle MD, Deustua S, Ellis RS, Fabbro S, Fruchter A, Goldhaber G, Groom DE, Hook IM, Kim AG, Kim MY, Knop RA, Lidman C, McMahon RG, Nugent P, Pain R, Panagia N, Pennypacker CR, Ruiz-Lapuente P, Schaefer B, Walton N (1998) Discovery of a supernova explosion at half the age of the Universe. Nature 391:51–54

    Article  ADS  Google Scholar 

  6. Perlmutter S, Aldering G, Goldhaber G, Knop RA, Nugent P, Castro PG, Deustua S, Fabbro S, Goobar A, Groom DE, Hook IM, Kim AG, Kim MY, Lee JC, Nunes NJ, Pain R, Pennypacker CR, Quimby R, Lidman C, Ellis RS, Irwin M, McMahon RG, Ruiz-Lapuente P, Walton N, Schaefer B, Boyle BJ, Filippenko AV, Matheson T, Fruchter AS, Panagia N, Newberg HJM, Couch WJ, and The Supernova Cosmology Project (1999) Measurements of \(\Omega \) and \(\Lambda \) from 42 high-redshift supernovae. Astrophys J 517:565–586

  7. Riess AG, Filippenko AV, Challis P, Clocchiatti A, Diercks A, Garnavich PM, Gilliland RL, Hogan CJ, Jha S, Kirshner RP, Leibundgut B, Phillips MM, Reiss D, Schmidt BP, Schommer RA, Smith RC, Spyromilio J, Stubbs C, Suntzeff NB, Tonry J (1998) Observational evidence from supernova for an acelerating universe and a cosmological constant. Astron J 116:1009–1038

    Article  ADS  Google Scholar 

  8. Riess AG, Strolger LG, Tonry J, Casertano S, Ferguson HC, Mobasher B, Challis P, Filippenko AV, Jha S, Li W, Chornock R, Kirshner RP, Leibundgut B, Dickinson M, Livio M, Giavalisco M, Steidel CC, Bentez T, Tsvetanov Z (2004) Type Ia supernova discoveries at \(z>1\) from the Hubble space telescope: evidence for past deceleration and constraints on dark energy evolution. Astrophys J 607:665–687

    Article  ADS  Google Scholar 

  9. Schmidt BP, Suntzeff NB, Phillips MM, Schommer RA, Clocchiatti A, Kirshner RP, Garnavich P, Challis P, Leibundgut B, Spyromilio J, Riess AG, Filippenko AV, Hamuy M, Smith RC, Hogan C, Stubbs C, Diercks A, Reiss D, Gilliland R, Tonry J, Maza J, Dressler A, Walsh J, Ciardullo R (1998) The high-Z supernova search: measuring cosmic deceleration and global curvature of the universe using type Ia supernovae. Astrophys J 507:46–63

    Article  ADS  Google Scholar 

  10. Peebles PJE, Ratra B (1998) Cosmology with a time-variable cosmological constant. Astrophys J 325:17–20

    Article  Google Scholar 

  11. Berman MS (1991) Cosmological models with a variable cosmological term. Phys Rev D 43:1075–1078

    Article  ADS  Google Scholar 

  12. Vishwakarma RG, Abdussattar Beesham A (1999) LRS Bianchi type-I models with a time-dependent cosmological constant. Phys Rev D 60:063507

    Article  ADS  MathSciNet  Google Scholar 

  13. Gasperini M (1987) Decreasing vacuum temperature: a thermal approach to the cosmological constant problem. Phys Lett B 194:347–349

    Article  ADS  Google Scholar 

  14. Gasperini M (1988) A thermal interpretation of the cosmological constant. Class Quant Gravit 5:521–536

    Article  ADS  MathSciNet  Google Scholar 

  15. Berman MS, Som MM (1990) Brans–Dicke models with time-dependent cosmological term. Int J Theor Phys 29:1411–1414

    Article  MathSciNet  Google Scholar 

  16. Pradhan A (2009) Some magnetized bulk viscous string cosmological models in cyllindrically symmetric inhomogeneous universe with variable \(\lambda \)-term. Commun Theor Phys 51:367–374

    Article  ADS  MATH  Google Scholar 

  17. Abdussattar Vishwakarma RG (1996) A model of the universe with decaying vacuum energy. Pramana J Phys 47:41–55

    Article  ADS  Google Scholar 

  18. Pradhan A, Yadav VK (2002) Bulk viscous anisotropic cosmological models with variable G and \(\Lambda \). Int J Mod Phys D11:893–912

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Eckart C (1940) The thermodynamics of irreversible processes, III. Relativistic theory of simple fluid. Phys Rev 58:919–924

    Article  ADS  MATH  Google Scholar 

  20. Landau LD, Lifshitz EM (1959) Fluid mechanics. Pergamon, New York

    MATH  Google Scholar 

  21. Weinberg S (1971) Entropy generation and the survival of protogalaxin an expanding universe. Astophys J 168:175–194

    Article  ADS  Google Scholar 

  22. Misner CW (1968) The isotropy of the universe. Astrophys J 151:431–457

    Article  ADS  Google Scholar 

  23. Patel LK, Sharada Koppar S (1991) Some Bianchi type \(VI_0\) viscous fluid cosmological models. J Austral Math Soc Ser B 33:77–84

    Article  MathSciNet  MATH  Google Scholar 

  24. Murphy GL (1973) Big-bang without singularities. Phys Rev D 8:4231–4233

    Article  ADS  Google Scholar 

  25. Klimek Z (1974) Some thermodynamic features of cosmological models with viscosity. Acta Cosmol 2:49–52

    ADS  Google Scholar 

  26. Banerjee A, Ribeiro MB, Santos NO (1987) Anisotropic viscous fluid cosmological models. Astrophys Space Sci 136:331–336

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. Dunn KA, Tupper BOJ (1978) Tilting and viscous models in a class of Bianchi type \(VI_0\) cosmologies. Astrophys J 222:405–411

    Article  ADS  Google Scholar 

  28. Roy SR, Prakash S (1978) Some viscous fluid cosmological models of plane symmetry. J Phys A 9:261–267

    Article  ADS  Google Scholar 

  29. Roy SR, Singh JP (1983) Some Bianchi type \(VI_0\) cosmological models with free gravitational field of the magnetic type. Acta Phys Austriaca 55:57–66

    ADS  MathSciNet  Google Scholar 

  30. Ribeiro MB, Sanyal AK (1987) Bianchi \(VI_0\) viscous fluid cosmology with magnetic fluid. J Math Phys 28:657–660

    Article  ADS  MathSciNet  MATH  Google Scholar 

  31. Santos NO, Dias RS, Banerjee A (1985) Isotropic homogeneous universe wih viscous fluid. J Math Phys 28:878–881

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. Johri VB, Sudarshan R (1988) FRW cosmological models with bulk viscosity and entropy production. In: Proceedings of the international conference on mathematical modelling in science and technology, vol 2. Tata McGraw-Hill

  33. Verma MK, Ram S (2011) Bianchi type \(VI_0\) bulk viscous fluid models with variable gravitational and cosmological constant. Appl Math 2:348–354

    Article  MathSciNet  Google Scholar 

  34. Sahni V, Starobinski A (2000) The case for a positive cosmological \(\Lambda \)-term. Int J Mod Phys D 9:373–443

    ADS  Google Scholar 

  35. Peebles PJE (2003) The cosmological constant and dark energy. Rev Mod Phys 75:559–606

    Article  ADS  MathSciNet  MATH  Google Scholar 

  36. Bali R, Pradhan A (2007) Bianchi type III string cosmological models with time dependent bulk viscosity. Chin Phys Lett 24:585–588

    Article  Google Scholar 

  37. Singh CP, Kumar S, Pradhan A (2007) Early viscous universe with variable gravitational and cosmological constant. Class Quant Grav 24:455–474

    Article  ADS  MathSciNet  MATH  Google Scholar 

  38. Pradhan A, Singh SK (2004) Bianchi type I magnetofluid cosmological models with variable cosmological constant revisited. Int J Mod Phys D 13:503–516

    Article  ADS  MathSciNet  MATH  Google Scholar 

  39. Barrow JD (1984) Helium formation in cosmologies with anisotropic curvature. Mon Not R Astron Soc 211:221–227

    Article  ADS  Google Scholar 

  40. Ellis GFR, MacCallum MAH (1969) A class of homogeneous cosmological models. Commun Math Phys 12:108–141

    Article  ADS  MathSciNet  MATH  Google Scholar 

  41. Dunn KA, Tupper BOJ (1976) A class of Bianchi type \(VI\) cosmological models with electromagnetic field. Astrophys J 204:322–329

    Article  ADS  Google Scholar 

  42. Amirhashchi H, Pradhan A, Saha B (2011) Variable equation of state for Bianchi type \(VI_0\) dark energy models. Astrophys Space Sci 333:295–303

    Article  ADS  Google Scholar 

  43. Pradhan A (2013) Accelerating dark energy models with anisotropic fluid in Bianchi type \(VI_0\) space–time. Res Astron Astrophys 13:139–158

    Article  ADS  Google Scholar 

  44. Ram Shri (1986) Perfect fluid models of Bianchi type \(VI_0\) in modified Brans–Dicke cosmology. J Math Phys 27:650–652

    Article  ADS  MathSciNet  Google Scholar 

  45. Radinschi I (2001) Energy associated with Bianchi type \(VI_0\) universe. Chin J Phys 39:393–396

    Google Scholar 

  46. Roy SR, Banerjee SK (1996) Bianchi \(VI_0\) electric type cosmological models in general relativity with stiff fluid and heat conduction. Gen Relativ Grav 28(1):27–33. doi:10.1007/BF02106851

    Article  ADS  MathSciNet  MATH  Google Scholar 

  47. Adhav KS, Bansod AS, Munde SL, Nakwal RG (2011) Bianchi type-\(VI_0\) cosmological models with anisotropic dark energy. Astrophys Space Sci 332:497–502

    Article  ADS  Google Scholar 

  48. Bali R, Banerjee R, Banerjee SK (2009) LRS Bianchi type \(VI_0\) cosmological models with specific free gravitional fields. Electron J Theor Phys 6:165–174

    Google Scholar 

  49. Kantowski J, Sachs RK (1966) Some spatially homogeneous anisotropic relativistic cosmological models. J Math Phys 7:443–446

    Article  ADS  MathSciNet  Google Scholar 

  50. Kristian J, Sachs RK (1966) Observations in cosmology. Astrophys J 143:379–399

    Article  ADS  MathSciNet  Google Scholar 

  51. Collins CB, Glass EN, Wilkinson DA (1980) Exact spatially homogeneous cosmologies. Gen Relativ Gravit 12:805–823

    Article  ADS  MathSciNet  MATH  Google Scholar 

  52. Saha B (2005) Bianchi type I universe with viscous fluid. Mod Phys Lett A 20:2127–2143

    Article  ADS  MathSciNet  MATH  Google Scholar 

  53. Mostafapoor N, Grøn O (2011) Viscous \(\Lambda \) CDM universe models. Astrophys Space Sci 333:357–368

    Article  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Prashant S. Baghel.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Singh, J.P., Baghel, P.S. & Singh, A. Bianchi Type VI 0 Viscous Fluid Cosmological Models with Time-Dependent Cosmological Term \(\varLambda \) . Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 86, 355–360 (2016). https://doi.org/10.1007/s40010-016-0280-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40010-016-0280-2

Keywords

Navigation