arXiv:2502.03483v1 Announce Type: new
Abstract: This thesis employs the dynamical systems approach to explore two cosmological models: an anisotropic dark energy scenario in a Bianchi-I background and the Generalized SU(2) Proca (GSU2P) theory in a flat FLRW background. In the first case, a numerical framework is developed to analyze the interaction between a scalar tachyon field and a vector field, identifying parameter regions that allow anisotropic accelerated attractors. The second case examines the viability of GSU2P as a driver of inflation and late-time acceleration. Our analysis reveals fundamental limitations, including the absence of stable attractors and smooth cosmological transitions, ultimately ruling out the model as a complete description of the Universe’s expansion. This work highlights the effectiveness of dynamical systems techniques in assessing alternative cosmological scenarios and underscores the need for refined theoretical frameworks aligned with observational constraints.
This thesis examines two cosmological models using the dynamical systems approach: an anisotropic dark energy scenario in a Bianchi-I background and the Generalized SU(2) Proca (GSU2P) theory in a flat FLRW background. The first case explores the interaction between a scalar tachyon field and a vector field, identifying parameter regions that allow anisotropic accelerated attractors. The second case investigates if GSU2P can drive inflation and late-time acceleration.
However, the analysis reveals fundamental limitations in both models. In the anisotropic dark energy scenario, stable attractors and smooth cosmological transitions are found to be absent, ruling out this model as a complete description of the Universe’s expansion. Similarly, GSU2P is also deemed inadequate in providing a complete understanding of cosmological phenomena.
Despite these limitations, this work demonstrates the effectiveness of dynamical systems techniques in assessing alternative cosmological scenarios. This research highlights the importance of refined theoretical frameworks that are aligned with observational constraints to further our understanding of the Universe’s expansion.
Future Roadmap
While the current models explored in this thesis may not provide a complete description of the Universe’s expansion, there are several opportunities for future research and development in the field. These include:
- Refining existing models: There is still scope for refining the anisotropic dark energy scenario and the GSU2P theory to overcome their limitations and potentially align them with observational constraints.
- Exploring other cosmological models: The dynamical systems approach can be applied to investigate other cosmological models and scenarios. By analyzing their attractors and transitions, we can gain valuable insights into the behavior of these models and their viability as complete descriptions of the Universe’s expansion.
- Integrating observational data: Future research should focus on incorporating observational data from cosmological surveys and experiments to further constrain and validate theoretical frameworks. This integration will enable a more comprehensive understanding of the Universe’s expansion.
- Developing new theoretical frameworks: Building on the insights gained from dynamical systems techniques, there is a need for the development of new theoretical frameworks that can better explain the observed cosmological phenomena. These frameworks should be able to account for the absence of stable attractors and smooth transitions found in the current models.
It is important for researchers to collaborate and share their findings to collectively advance our understanding of cosmology. By embracing the challenges and opportunities of refining and developing theoretical frameworks, we can strive towards a comprehensive and accurate description of the Universe’s expansion.