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Stability analysis of anisotropic Bianchi type I cosmological model

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Abstract

Locally Rotationally Symmetric(LRS) Bianchi type I cosmological model interacting with scalar field and exponential potential is presented and phase plane analysis is done in the framework of dynamical systems. Evolution equations are analyzed and reduced to a system of ordinary differential equations which are autonomous by suitable variable transformations. All critical points both hyperbolic and non hyperbolic of the system are listed and their stability properties are analyzed and examined from the cosmological point of view. For non hyperbolic points perturbation theory is applied. Some representations of phase diagrams are shown explicitly.

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References

  1. Mishra, B., et al.: Dynamical features of an anisotropic cosmological model. Indian J. Phys. 92, 1199–1206 (2018). https://doi.org/10.1007/s12648-018-1194-4

    Article  ADS  CAS  Google Scholar 

  2. Saadeh, D., et al.: How isotropic is the Universe. Phys. Rev. Lett. 117, 131302 (2016). https://doi.org/10.1103/PhysRevLett.117.131302

    Article  ADS  CAS  PubMed  Google Scholar 

  3. De Bernardis, P., et al.: A Flat universe from high resolution maps of the cosmic microwave background radiation. Nature 404, 955 (2000). https://doi.org/10.1038/35010035

    Article  ADS  CAS  Google Scholar 

  4. Stompor, R., et al.: Cosmological implications of the MAXIMA-1 high-resolution cosmic microwave background anisotropy measurement. Astroph. J. 561, 7 (2001). https://doi.org/10.1086/324438

    Article  Google Scholar 

  5. Chaubey, R., et al.: Bianchi Type-I Universe with wet dark fluid. Pramana - J Phys 71, 447–458 (2008). https://doi.org/10.1007/s12043-008-0124-y

    Article  ADS  Google Scholar 

  6. Perlmutter, S., et al.: The Supernova Cosmology Project Cosmology from Type Ia Supernovae. Bull. Am. Astron. Soc. 29, 1351 (1997)

    ADS  Google Scholar 

  7. Perlmutter, S., et al.: Discovery of a supernova explosion at half the age of the Universe. Nature 391, 51–54 (1998). https://doi.org/10.1038/34124

    Article  ADS  CAS  Google Scholar 

  8. Perlmutter, S., et al.: Measurements of \(\Omega \) and \(\Lambda \) from 42 High-Redshift Supernovae. ApJ 517, 565 (1999). https://doi.org/10.1086/307221

    Article  ADS  Google Scholar 

  9. Garnavich, P.M., et al.: Constraints on cosmological models from Hubble Space Telescope observations of high-z supernovae. ApJ 493, L53 (1998). https://doi.org/10.1086/311140

    Article  ADS  Google Scholar 

  10. Garnavich, P.M., et al.: Supernova limits on the cosmic equation of state. ApJ 509(1), 74–79 (1998). https://doi.org/10.1086/306495

    Article  ADS  CAS  Google Scholar 

  11. Riess, A.G., et al.: Type Ia Supernova Discoveries at \(z > 1\) from the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution. ApJ 607, 665 (2004). https://doi.org/10.1086/383612

    Article  ADS  CAS  Google Scholar 

  12. Torny, J.L., et al.: Cosmological results from High-z Supernovae. ApJ 594, 1 (2003). https://doi.org/10.1086/376865

    Article  ADS  Google Scholar 

  13. Spergel, D.N., et al.: First-year Wilkinson microwave anisotropy probe (WMAP)* observations: Determination of cosmological parameters. ApJS 148, 175–194 (2003). https://doi.org/10.1086/377226

    Article  ADS  Google Scholar 

  14. Angit, S., et al.: Universe with wet dark fluid: a dynamical systems approach. Int. J. Geom. Methods Mod. Phys. 168, 1950127 (2019). https://doi.org/10.1142/S0219887819501275

    Article  MathSciNet  Google Scholar 

  15. Sonia, C., Singh, S.S.: Dynamical systems of cosmological models for different possibilities of \(G\) and \(\rho _{\Lambda }\). Eur. Phys. J. C 82, 863 (2022). https://doi.org/10.1140/epjc/s10052-022-10826-8

    Article  ADS  CAS  Google Scholar 

  16. Samaddar, A., Singh,S.S.: Qualitative stability analysis of cosmological parameters in \(f(T,B) gravity\). Eur. Phys. J. C 83, 283 (2023). https://doi.org/10.1140/epjc/s10052-023-11458-2

  17. Chaubey, R., Raushan, R.: Dynamical analysis of anisotropic cosmological model with quadratic dark sector coupling. Int. J. Geom. Methods Mod. Phys. 16, 02 (2019). https://doi.org/10.1007/S10509-016-2806-0

    Article  MathSciNet  Google Scholar 

  18. Luongo, O., Quevedo, H.: An expanding Universe with constant pressure and nocosmological constant. Astrophys. Space Sci. 338, 345 (2012). https://doi.org/10.1007/s10509-011-0937-x

    Article  ADS  Google Scholar 

  19. Luongo, O., Quevedo, H.: Characterizing repulsive gravity with curvature eigenvalues. Phys. Rev. D 90, 084032 (2014). https://doi.org/10.1103/PhysRevD.90.084032

    Article  ADS  CAS  Google Scholar 

  20. Luongo, O., Quevedo, H.: A unified dark energy model from a vanishing speed of sound with emergent cosmological constant. Int. J. Mod. Phys. D 23, 02 (2014). https://doi.org/10.1142/S0218271814500126

    Article  CAS  Google Scholar 

  21. Luongo, O. , Muccino, M.: Speeding up the Universe using dust with pressure. Phys. Rev. D 98, 10 (2018). https://doi.org/10.1103/PhysRevD.98.103520

  22. Caldwell, R.R., et al.: Cosmological Imprint of an Energy Component with General Equation of State. Phys. Rev. Lett. 80, 1582–1585 (1998)

    Article  ADS  CAS  Google Scholar 

  23. Sonia, C., Singh, S. S.: Dynamical system perspective of cosmological models minimally coupled with scalar field. Adv. High Energy Phys. 2020, 1805350 (2020). https://doi.org/10.1155/2020/1805350

  24. Chaubey, R., et al.: Dynamical analysis of anisotropic cosmological model with quintessence. Astrophys. Space Sci. 361, 215 (2016). https://doi.org/10.1103/PhysRevLett.80.1582

    Article  ADS  MathSciNet  Google Scholar 

  25. Ferreira, P. G., Joyce, M.: Structure Formation with a Self-Tuning Scalar Field. Phys. Rev. Lett.79, 24 (1997). https://doi.org/10.1103/PhysRevLett.79.4740

  26. Basilakos, S., et al.: Scalar field theory description of the running vacuum model: the vacuumon. JCAP 12, 025 (2019). https://doi.org/10.1088/1475-7516/2019/12/025

  27. Chan, N.: Dynamical systems in cosmology (Doctoral dissertation. UCL (University College London) (2012). https://doi.org/10.1142/9781786341044-0004

    Article  PubMed Central  Google Scholar 

  28. Salcedo, R.G., et al.: Introduction to the application of dynamical systems theory in the study of the dynamics of cosmological models of dark energy. Eur. J. Phys. 36, 025008 (2015). https://doi.org/10.1088/0143-0807/36/2/025008

    Article  Google Scholar 

  29. Wainwright, J., Ellis, G. F. R.: Dynamical Systems in Cosmology. Cambridge University Press(1997). https://doi.org/10.1017/CBO9780511524660

  30. Bahamonde, S., et al.: Dynamical systems applied to cosmology: dark energy and modified gravity. Phys. Rep. 775–777, 1–122 (2018). https://doi.org/10.1016/j.physrep.2018.09.001

    Article  ADS  MathSciNet  Google Scholar 

  31. Shah, P., et al.: Stability analysis for cosmological models in \(f(R)\) gravity using dynamical system analysis. Eur. Phys. J. C 79, 414 (2019). https://doi.org/10.1140/epjc/s10052-019-6934-x

    Article  ADS  CAS  Google Scholar 

  32. Boehmer, et al.: Jacobi stability analysis of dynamical systems applications in gravitation and cosmology. Adv. Theor. Math 16(4), 1145–1196 (2012). https://doi.org/10.4310/ATMP.2012.V16.N4.A2

  33. Demianski, M. et al.: Scalar fields and anisotropy in cosmological models. Phys. Rev. D 46, 1391 (1992). https://doi.org/10.1103/PhysRevD.46.1391

  34. Goheer, N., et al.: Dynamical systems analysis of anisotropic cosmologies in \(R^{n}\)-gravity. Class. Quantum Grav 24, 5689 (2007). https://doi.org/10.1088/0264-9381/24/22/026

    Article  ADS  MathSciNet  Google Scholar 

  35. Shivangi Rathore, S., Singh, 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 

  36. Samaddar, A., Singh, S.S., Alam, M.K.: Dynamical system approach of interacting dark energymodels with minimally coupled scalar field. Int. J. Mod. Phys. D 9(32), 2350062 (2023). https://doi.org/10.1142/S0218271823500621

    Article  Google Scholar 

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Acknowledgements

We would like to thank the anonymous referee for valuable suggestions and advices.

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

    Sreelakshmi Pillai & Sanasam Surendra Singh

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  1. Sreelakshmi Pillai
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  2. Sanasam Surendra Singh
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Correspondence to Sreelakshmi Pillai.

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Pillai, S., Singh, S.S. Stability analysis of anisotropic Bianchi type I cosmological model. Afr. Mat. 35, 23 (2024). https://doi.org/10.1007/s13370-023-01162-5

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