Skip to main content
SpringerLink
Log in

Finsler–Randers Cosmological Models in Modified Gravity Theories

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

Abstract

Finsler–Randers (FR) cosmological models in modified gravity theories have been investigated in this paper. The de Sitter and power law solutions are assumed for the scale factor in the corresponding cosmological models. All energy conditions have been discussed in detail for each scenario. Behaviour of FR cosmological models in modified theories of gravity like Einstein theory, Hoyle–Narlikar creation field theory, lyra geometry and general class of scalar–tensor theories have also been investigated.

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. Randers G (1941) On an asymmetrical metric in the four-space of general relativity. Phys. Rev. 59:195–199

    Article  ADS  MathSciNet  Google Scholar 

  2. Ellis GFR, Van Elst H (1999) In: Lachièze-Rey M (ed) NATO ASIC proc. 541: theoretical and observational cosmology.arxiv: gr-qc/9812046

  3. Hawking SW, Ellis GFR (1973) The large scale structure of space-time. Cambridge University Press, Cambridge

    Book  Google Scholar 

  4. Belinskii VA, Khalatnikov IM, Lifshits EM (1970) Oscillatory approach to a singular point in the relativistic cosmology. Adv Phys 19:525

    Article  ADS  Google Scholar 

  5. Misner CW (1968) The spatial relativity and its physical consequences. Astrophys J 151:431

    Article  ADS  Google Scholar 

  6. MacCallum MAH (1979) Anisotropic and inhomogeneous relativistic cosmologies. In: Hawking SW, Israel W (eds) General relativity: an einstein centenary survey (chapter 11). Cambridge University Press, Cambridge

    Google Scholar 

  7. Ellis GFR (1993) Exact and inexact solutions of the Einstein field equations. In: Ellis G, Lanza A, Miller J (eds) The renaissance of general relativity and cosmology, p 20

    Chapter  Google Scholar 

  8. Kolb EW, Turner MS (1990) The early universe. Addison-Wesley, Boston

    MATH  Google Scholar 

  9. Misner CW, Thorne KS, Wheeler JA (1973) Gravitation. WH Freeman, New York

    Google Scholar 

  10. Hu BL, Parker L (1978) Anisotropy damping through quantum effects in the early universe. Phys Rev D 17:933

    Article  ADS  Google Scholar 

  11. Stavrinos PC, Kouretsis A, Stathakopoulos M (2008) Friedmann Robertson–Walker model in generalised metric space-time with weak anisotropy. Gen Relativ Gravit 40:1404

    Article  ADS  Google Scholar 

  12. Basilakos S, Stavrinos P (2013) Cosmological equivalence between the Finsler-Randers space-time and the DGP gravity model. Phys Rev D 87:043506 arxiv:1301.4327v2 [gr-qc]

    Article  ADS  Google Scholar 

  13. Rund H (1959) The differential geometry of Finlser spaces. Springer, Berlin

    Book  Google Scholar 

  14. Miron R, Anastasiei M (1994) The geometry of Lagrange spaces: theory and applications. Kluwer Academic, Dordrecht

    Book  Google Scholar 

  15. Bao D, Chern SS, Shen Z (2000) An introduction to Riemann-Finsler geometry. Springer, New York

    Book  Google Scholar 

  16. Vacaru S, Stavrinos PC, Gaburov E, Gonta D (2005) Clifford and Riemann-Finsler structures in geometric mechanics and gravity. Geometry Balkan Press, Bucharest

    MATH  Google Scholar 

  17. Kolassis A, Santos NO, Tsoubelis D (1988) Energy conditions for an imperfect fluid. Class Quantum Gravity 5:1329

    Article  ADS  MathSciNet  Google Scholar 

  18. Chatterjee S, Banerjee A (2004) C-field cosmology in higher dimensions. Gen Relativ Gravit 36:303

    Article  ADS  MathSciNet  Google Scholar 

  19. Bali R, Saraf S (2013) C-field cosmological model for barotropic fluid distribution with bulk viscosity and decaying vacuum energy () in FRW spacetime. Can J Phys 91:728

    Article  ADS  Google Scholar 

  20. Arbab AI (2007) Viscous dark energy models with variable G and lambda. arXiv:gr-qc/0711.2292

  21. Padmanabhan T (2002) Accelerated expansion of the universe driven by tachyonic matter. Phys Rev D 66:021301

    Article  ADS  Google Scholar 

  22. Lyra G (1951) Über eine modifikation der riemannschen geometrie. Z Phys 54:52

    MathSciNet  MATH  Google Scholar 

  23. Hoyle F, Narlikar JV (1962) Mach’s principle and the creation of matter. Proc R Soc Lond A 270:334

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors AKS and MK express their thank to N.B.H.M., Mumbai for the financial assistance under the Post-Doctoral Scheme. One of the authors (RC) express their thanks to C.S.I.R., New Delhi for the financial assistance under the Project No. P-25(0259)/17/EMR-II.

Author information

Authors and Affiliations

  1. DST-Centre for Interdisciplinary Mathematical Sciences, Institute of Science, Banaras Hindu University, Varanasi, India

    R. Chaubey, B. Tiwari, Anjani Kumar Shukla & Manoj Kumar

Authors
  1. R. Chaubey
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. Tiwari
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anjani Kumar Shukla
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Manoj Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Chaubey.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chaubey, R., Tiwari, B., Kumar Shukla, A. et al. Finsler–Randers Cosmological Models in Modified Gravity Theories. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 89, 757–768 (2019). https://doi.org/10.1007/s40010-018-0534-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40010-018-0534-2

Keywords

Search

Navigation