Cosmological dynamics are investigated in detail through systematic
procedures by using the autonomous system analyses of gravitational field
equations in higher-order symmetric teleparallel equivalent of general
relativity. The explicit analyses of the late-time cosmic evolutions are
demonstrated for fundamental three types of models under the presence of
non-relativistic matter (i.e., dark matter and baryons) as well as radiation.
The stability of cosmological solutions is also explored by examining
non-hyperbolic critical points based on the center manifold theory. It is shown
that the acceleration of the universe can be achieved with the higher curvature
gravity. Three different models were considered for the study and dynamical
systems analysis technique is incorporated. The main finding of the present
analyses is that cosmological solutions in higher-order symmetric teleparallel
equivalent of general relativity can effectively fit observable datasets. This
is depicted by phase space portraits and qualitative evolution of the
cosmological models.
Future Roadmap for Cosmological Dynamics in Higher-order Symmetric Teleparallel Equivalent of General Relativity
In this article, the author examines the cosmological dynamics in detail through systematic procedures using the autonomous system analyses of gravitational field equations in higher-order symmetric teleparallel equivalent of general relativity. The explicit analyses focus on the late-time cosmic evolutions and the stability of cosmological solutions under the presence of non-relativistic matter and radiation.
The main conclusion of the study is that acceleration of the universe can be achieved with the higher curvature gravity, and cosmological solutions in higher-order symmetric teleparallel equivalent of general relativity can effectively fit observable datasets. The findings are supported by phase space portraits and qualitative evolution of the cosmological models.
Future Challenges
- Model refinement: Further refinement of the three different models studied will be necessary to improve the accuracy of fitting observable datasets. The incorporation of additional variables or adjusting existing parameters may be required.
- Data validation: The observational data used to validate the models should be carefully analyzed and verified for consistency and accuracy. Robust statistical methods should be employed to ensure reliable comparisons.
- Testing alternative theories: While higher-order symmetric teleparallel equivalent of general relativity shows promise, it is important to explore and test alternative theories to gain a comprehensive understanding of cosmological dynamics. This will involve comparing the predictions and outcomes of different theoretical frameworks.
- Computational challenges: The complexity of the analyses and simulations involved in investigating cosmological dynamics pose computational challenges. Advancements in computational power and algorithms will be crucial to overcome these hurdles.
Potential Opportunities
- Cosmological model validation: The ability to effectively fit observable datasets using higher-order symmetric teleparallel equivalent of general relativity opens up opportunities for the validation of cosmological models and theories.
- Understanding dark matter and acceleration: The achievement of universe acceleration through higher curvature gravity provides insights into the nature and behavior of dark matter. This can contribute to our understanding of the fundamental properties of the universe.
- Innovations in gravitational field equations: The systematic procedures and analyses used in this study can pave the way for innovations in gravitational field equations. This may lead to the development of new theoretical frameworks and models for cosmological dynamics.
- Interdisciplinary collaborations: Cosmological dynamics involve concepts from various disciplines such as physics, mathematics, and astronomy. The findings of this study can foster interdisciplinary collaborations and stimulate further research in these fields.
Overall, the findings of this study contribute to the understanding of cosmological dynamics in higher-order symmetric teleparallel equivalent of general relativity and present avenues for future research. Further refinement of the models, validation of data, testing of alternative theories, and advancements in computational techniques are important challenges to address. However, the opportunities for model validation, insights into dark matter and acceleration, innovations in gravitational field equations, and interdisciplinary collaborations hold great potential for advancing our understanding of the universe.