Skip to main content
SpringerLink
Log in

Perfect fluid cosmological Universes: One equation of state and the most general solution

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

Considering a homogeneous and isotropic Universe characterised by the Friedmann–Lemaître–Robertson–Walker line element, in this work, we have prescribed a general formalism for the cosmological solutions when the equation of state of the cosmic substance follows the general structure \(\phi (p, \rho ) = 0\), where \(p,\,\rho \) are respectively the pressure and the energy density of the cosmic substance. Using the general formalism we recover some well-known solutions, namely, when the cosmic substance obeys the linear equation of state, a Chaplygin-type equation of state, or a nonlinear equation of state. Thus, the current work offers a new technique to solve the cosmological solutions without any prior relation between p and \(\rho \).

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A Das and A De Benedictis, The general theory of relativity: A mathematical exposition (Springer, New York, 2012)

    Book  Google Scholar 

  2. A K Raychaudhuri, S Banerjee and A Benerjee, General relativity, astrophysics, and cosmology (Springer, New York, 1992)

    Book  Google Scholar 

  3. J E Marsden and A J Tromba, Vector calculus, 3rd edn (W. H. Freeman & Co., New York, 1988)

    MATH  Google Scholar 

  4. S W Hawking and G F R Ellis, The large scale structure of space-time (Cambridge University Press, Cambridge, 1973)

    Book  MATH  Google Scholar 

  5. S Weinberg, Gravitation and cosmology: Principles and applications of the general theory of gravitation (Wiley, New York, 1972)

    Google Scholar 

  6. U Debnath, A Banerjee and S Chakraborty, Class. Quant. Grav.  21, 5609 (2004)

    Article  ADS  Google Scholar 

  7. J D Barrow, Phys. Lett. B  235, 40 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  8. S Nojiri and S D Odintsov, Phys. Rev. D  70, 103522 (2004), arXiv:hep-th/0408170

    Article  ADS  Google Scholar 

  9. S Nojiri, S D Odintsov and S Tsujikawa, Phys. Rev. D  71, 063004 (2005), arXiv:hep-th/0501025

    Article  ADS  Google Scholar 

  10. S Nojiri and S D Odintsov, Phys. Rev. D  72, 023003 (2005), arXiv:hep-th/0505215

    Article  ADS  Google Scholar 

  11. K Bamba, S Capozziello, S Nojiri and S D Odintsov, Astrophys. Space Sci.  342, 155 (2012)

    Article  ADS  Google Scholar 

  12. K Bamba, J de Haro and S D Odintsov, J. Cosmol. Astropart. Phys.  1302, 008 (2013)

    Article  ADS  Google Scholar 

  13. P H Frampton, K J Ludwick and R J Scherrer, Phys. Rev. D  84, 063003 (2011)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

SP acknowledges Science and Engineering Research Board (SERB), Govt. of India for National Post-Doctoral Fellowship (File No. PDF / 2015 / 000640). Also, SP thanks the Department of Mathematics, Jadavpur University where a part of the work was carried out.

Author information

Authors and Affiliations

  1. Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada

    Anadijiban Das

  2. Department of Physics, Jadavpur University, Kolkata, 700 032, India

    Asit Banerjee

  3. Department of Mathematics, Jadavpur University, Kolkata, 700 032, India

    Subenoy Chakraborty

  4. Department of Physical Sciences, Indian Institute of Science Education and Research, Kolkata, Mohanpur, 741 246, India

    Supriya Pan

Authors
  1. Anadijiban Das
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Asit Banerjee
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Subenoy Chakraborty
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Supriya Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Supriya Pan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Das, A., Banerjee, A., Chakraborty, S. et al. Perfect fluid cosmological Universes: One equation of state and the most general solution. Pramana - J Phys 90, 19 (2018). https://doi.org/10.1007/s12043-017-1511-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12043-017-1511-z

Keywords

PACS Nos

Search

Navigation