Skip to main content
SpringerLink
Log in

Stability aspects of an LRS Bianchi type-I cosmological model in f(Q) gravity

  • Research
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

This work deals with the dynamical system analysis of the Locally Rotationally Symmetric Bianchi type-I cosmological model in f(Q) gravity (where Q is the non-metricity). Here we Constructed cosmological models in f(Q) gravity which is based on the propositions of forms of f(Q). For the model, we take \(f(Q)=Q+\xi Q^{2}\) where \(\xi \) is constant. We reduce the evolution equation to an autonomous system of ordinary differential equations by appropriate substitution of the variables to setup the corresponding dynamical system and then we calculate the critical points for the model and examine their stability. We find out that we get four critical points, out of these, one critical point is stable and other three critical points are saddle points. And corresponding to the critical points A and B, our model corresponds to the quintessence dark energy cosmological model while the critical points C and D correspond to the phantom dark energy model. We also present the phase plot analysis for the derived model.

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

Fig. 1

Similar content being viewed by others

Data Availability

No data associated in the manuscript.

References

  1. Addazi, A., et al.: Quantum gravity phenomenology at the dawn of the multi-messenger era-A review. Prog. Part. Nucl. Phys. 125, 103948 (2022)

    Article  Google Scholar 

  2. Abdalla, E. et al.: Cosmology intertwined: a review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies, arXiv:2203.06142

  3. Lusso, E., Piedipalumbo, E., Risaliti, G., Paolillo, M., Bisogni, S., Nardini, E., Amati, L.: Tension with the flat \(\Lambda \)CDM model from a high-redshift Hubble diagram of supernovae, quasars, and gamma-ray bursts. Astron. Astrophys. 628, L4 (2019)

    Article  ADS  CAS  Google Scholar 

  4. Perivolaropoulos, L., Skara, F.: Challenges for \(\Lambda \)CDM: an update, arXiv:2105.05208

  5. Clifton, T., Ferreira, P.G., Padilla, A., Skordis, C.: Modified gravity and cosmology. Phys. Rep. 513, 1–189 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  6. Capozziello, S., De Laurentis, M.: Extended theories of gravity. Phys. Rep. arXiv:1108.6266

  7. Cai, Y.-F., Saridakis, E.N., Setare, M.R., Xia, J.-Q., Cosmology, Q.: Theoretical implications and observations. Phys. Rep. 493, 1–60 (2010)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  8. Joyce, A., Lombriser, L., Schmidt, F.: Dark energy versus modified gravity. Ann. Rev. Nucl. Part. Sci. 66, 95–122 (2016)

    Article  ADS  CAS  Google Scholar 

  9. Copeland, E.J., Sami, M., Tsujikawa, S.: Dynamics of dark energy. Int. J. Mod. Phys. D 15, 1753–1936 (2006)

  10. Riess, A.G., et al.: Astron J. 116, 1009 (1998)

    Article  ADS  Google Scholar 

  11. Perlmutter, S., et al.: Astrophys. J. 517, 565 (1999)

    Article  ADS  Google Scholar 

  12. Ade, P.A.R., et al.: Astron. Astrophys. 594, A13 (2016)

    Article  Google Scholar 

  13. Aldrovandi, R., Pereira, J.: Teleparallel Gravity. An Introduction, Fundamental Theories of Physics Vol. 173 (Springer, Dordrecht, 2014)

  14. Hinshaw, G., et al.: Astrophys. J. Suppl. 148, 135 (2003)

    Article  ADS  Google Scholar 

  15. Hinshaw, G., et al.: Astrophys. J. Suppl. 170, 288 (2007)

    Article  ADS  Google Scholar 

  16. Hinshaw, G., et al.: Astrophys. J. Suppl. 180, 225 (2009)

    Article  ADS  Google Scholar 

  17. Pitrou, C., Pereira, T.S., Uzan, J.P.: JCAP 0804, 004 (2008)

    Article  ADS  Google Scholar 

  18. Fadragas, C.R., Leon, G., Saridakis, E.N.: Class. Quantum Gravity 31, 075018 (2014)

  19. Jaffe, T.R., et al.: Astrophys. J. 643, 616 (2006)

    Article  ADS  Google Scholar 

  20. Jaffe, T.R., et al.: Astron. Astrophys. 460, 393 (2006)

    Article  ADS  Google Scholar 

  21. Campanelli, L., Cea, P., Tedesco, L.: Phys. Rev. D 76, 063007 (2007)

  22. Guth, A.H.: Phys. Rev. D 23, 347 (1981)

    Article  ADS  CAS  Google Scholar 

  23. Linde, A.D.: Phys. Lett. B 108, 389 (1982)

    Article  ADS  Google Scholar 

  24. Linde, A.D.: Phys. Lett. B 129, 177 (1983)

    Article  ADS  Google Scholar 

  25. Linde, A.D.: Phys. Lett. B 259, 38 (1991)

    Article  ADS  CAS  Google Scholar 

  26. Linde, A.D.: Phys. Rev. D 49, 748 (1994)

    Article  ADS  CAS  Google Scholar 

  27. Amirhashchi, H., Amirhashchi, S.: Phys. Dark Univ. 29, 100557 (2020)

  28. Amirhashchi, H.: Phys. Rev. D 96, 123507 (2017)

  29. Amirhashchi, H.: Phys. Rev. D 97, 063515 (2018)

  30. Riess, A.G., et al.: Astron. J. 116, 1009 (1998)

    Article  ADS  Google Scholar 

  31. Hohmann, M., Pfeifer, C., Ualikhanova, U., Levi Said, J.: Phys. Rev. D, 99, 024009 (2019)

  32. Lazkoz, R., et al.: Phys. Rev. D 100, 104027 (2018)

  33. Lin, R.-H., et al.: Phys. Rev. D 103, 124001 (2021)

  34. Khyllep, W., Paliathansis, A., Dutta, J.: Phys. Rev. D 103, 103521 (2021)

  35. Khyllep, W., Dutta, J., Saridakis, E.N., Yesmakhanova, K.: arXiv:2207.02610 [gr-qc]

  36. De, A., Mandal, S., Beh, J.T., Loo, T.H., Sahoo, P.K.: Isotropization of locally rotationally symmetric Bianchi-I Universe in \(f(Q)\)-gravity. Eur. Phys. J. C (2022) arXiv:2201.05036 [gr-qc]

  37. Schrödinger, E.: Space-time Structure. Cambridge University Press, Cambridge (1950)

    Google Scholar 

  38. Maluf, J.W.: Ann. Phys. 525, 339 (2013)

    Article  MathSciNet  Google Scholar 

  39. Golovnev, A., Koivisto, T.: JCAP 11, 012 (2018)

    Article  ADS  Google Scholar 

  40. Koivisto, T., Tsimperis, G.: Universe 5, 80 (2018)

    Article  ADS  Google Scholar 

  41. Jiménez, J.B., et al.: Phys. Rev. D 101, 103507 (2020)

  42. Linder, E.V.: Phys. Rev. D 81, 127301 (2010)

  43. Jimenez, J.B., Heisenberg, L., Koivisto, T.: Phys. Rev. D 98, 044048 (2018)

  44. Hehl, F.W., et al.: Phys. Rep. 258, 1 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  45. Rathore, S., Singh, S.S.: Dynamical system analysis of interacting dark energy in LRS Bianchi type I cosmology. Sci Rep 13, 13980 (2023). https://doi.org/10.1038/s41598-023-40457-2

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  46. Singh, S.S., Sonia, C.: Dynamical system perspective of cosmological models minimally coupled with scalar field, arXiv:1906.11947

  47. Samaddar, A., Singh, S.S., Alam, M.K.: Dynamical system approach of interacting dark energy models with minimally coupled scalar field. https://doi.org/10.1142/S0218271823500621

  48. Starobinsky, A.A.: Phys. Lett. B 91, 99 (1980)

    Article  ADS  Google Scholar 

  49. Anagnostopoulos, F.K., Basilakos, S., Saridakis, E.N.: First evidence that non-metricity \(f(Q)\) gravity could challenge CDM arXiv:2104.15123

  50. Bennett, C.L., et al.: ApJS 208, 20 (2013)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, National Institute of Technology Manipur, Imphal, 795004, India

    Shivangi Rathore & S. Surendra Singh

Authors
  1. Shivangi Rathore
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Surendra Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shivangi Rathore.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rathore, S., Singh, S.S. Stability aspects of an LRS Bianchi type-I cosmological model in f(Q) gravity. Gen Relativ Gravit 56, 25 (2024). https://doi.org/10.1007/s10714-024-03215-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10714-024-03215-x

Keywords

Search

Navigation