Anisotropies in Relativistic Cosmology

Benjamin Farrell

doi:10.59973/emjsr.392

Authors

Benjamin Farrell University of Portsmouth, Faculty of Technology, School of Mathematics and Physics, Portsmouth, PO1 3QL, UK https://orcid.org/0009-0005-7544-4129

DOI:

https://doi.org/10.59973/emjsr.392

Keywords:

Cosmology, Dynamical Systems, Dark Energy

Abstract

The aim of this study is to investigate the behaviour of anisotropic cosmological models over the age of the universe and the effect of different forms of dark energy on this behaviour. The Bianchi–I model is explored with field equations that are solved numerically, and the resulting behaviour of key quantities such as the scale factor, expansion rate, and shear is analysed and compared with that of the standard ΛCDM cosmology, as well as extending the model to include a non-linear dark energy component. The results show that the universe evolves from an early-time regime dominated by matter and anisotropies to a late-time one. The expansion rate in the early universe is modified by the quadratic term, resulting in a modified expansion
rate.

References

[1] Saadeh D, Feeney SM, Pontzen A, Peiris HV, McEwen JD. A framework for testing isotropy with the cosmic microwave background. Mon. Not. Roy. Astron. Soc. 2016;462(2):1802–1811. https://doi.org/10.1093/mnras/stw1731. DOI: https://doi.org/10.1093/mnras/stw1731

[2] Stephani H. Relativity: An Introduction to Special and General Relativity. 2004. DOI: https://doi.org/10.1017/CBO9780511616532

[3] Ananda KN, Bruni M. Cosmo-dynamics and dark energy with a quadratic EoS: Anisotropic models, large-scale perturbations and cosmological singularities. Phys. Rev. D. 2006;74:023524. https://doi.org/10.1103/PhysRevD.74.023524. DOI: https://doi.org/10.1103/PhysRevD.74.023524

[4] Wolfram Research, Inc. Mathematica, Version 14.3. Champaign, IL; 2025. https://www.wolfram.com/mathematica.

[5] Saadeh D, Feeney SM, Pontzen A, Peiris HV, McEwen JD. How isotropic is the Universe? Phys. Rev. Lett. 2016;117(13):131302.

https://doi.org/10.1103/PhysRevLett.117.131302. DOI: https://doi.org/10.1103/PhysRevLett.117.131302

[6] Wang YY, Wang FY. Testing the isotropy of the Universe with type Ia supernovae in a model-independent way. Mon. Not. Roy. Astron. Soc. 2018;474(3):3516–3522. https://doi.org/10.1093/mnras/stx2982. DOI: https://doi.org/10.1093/mnras/stx2982

[7] Verma A, Aluri PK, Mota DF. Anisotropic universe with anisotropic dark energy. Phys. Rev. D. 2025;111(8):083508.

https://doi.org/10.1103/PhysRevD.111.083508. DOI: https://doi.org/10.1103/PhysRevD.111.083508

[8] Akarsu ¨O, Kumar S, Sharma S, Tedesco L. Constraints on a Bianchi type I spacetime extension of the standard ΛCDM model. Phys. Rev. D. 2019;100(2):023532. https://doi.org/10.1103/PhysRevD.100.023532. DOI: https://doi.org/10.1103/PhysRevD.100.023532

[9] Sarmah P, Goswami UD. Bianchi Type I model of universe with customized scale factors. Mod. Phys. Lett. A. 2022;37(21):2250134. https://doi.org/10.1142/S0217732322501346. DOI: https://doi.org/10.1142/S0217732322501346