arXiv:2402.07951v1 Announce Type: new
Abstract: The higher-curvature gravity with boundary terms i.e the $f(Q)$ theories, grounded on non-metricity as a fundamental geometric quantity, exhibit remarkable efficacy in portraying late-time universe phenomena. The aim is to delineate constraints on two prevalent models within this framework, namely the Log-square-root model and the Hyperbolic tangent-power model, by employing the framework of Big Bang Nucleosynthesis (BBN). The approach involves elucidating deviations induced by higher-curvature gravity with boundary terms in the freeze-out temperature ($T_{f}$) concerning its departure from the standard $Lambda$CDM evolution. Subsequently, constraints on pertinent model parameters are established by imposing limitations on $vert frac{delta T_{f}}{T_{f}}vert$ derived from observational bounds. This investigation employs dynamical system analysis, scrutinizing both background and perturbed equations. The study systematically explores the phase space of the models, identifying equilibrium points, evaluating their stability, and comprehending the system’s trajectory around each critical point. The principal findings of this analysis reveal the presence of a matter-dominated saddle point characterized by the appropriate matter perturbation growth rate. Subsequently, this phase transitions into a stable phase of a dark-energy-dominated, accelerating universe, marked by consistent matter perturbations. Overall, the study substantiates observational confrontations, affirming the potential of higher-curvature gravity with boundary terms as a promising alternative to the $Lambda$CDM concordance model. The methodological approach underscores the significance of dynamical systems as an independent means to validate and comprehend the cosmological implications of these theories.
Future Roadmap
1. Further Exploration of $f(Q)$ Theories
The study highlights the efficacy of $f(Q)$ theories in portraying late-time universe phenomena. Future research should continue to explore these theories and their implications for a deeper understanding of the universe.
2. Investigation of Other Models within the $f(Q)$ Framework
While this study focused on the Log-square-root model and the Hyperbolic tangent-power model, there are likely other models within the $f(Q)$ framework that could be explored. Future research should investigate these alternative models to expand our knowledge of higher-curvature gravity with boundary terms.
3. Further Constraints on Model Parameters
Constraints on model parameters were established using limitations on $vert frac{delta T_{f}}{T_{f}}vert$ derived from observational bounds. Further research should aim to refine and strengthen these constraints, potentially using additional observational data or improved techniques.
4. Exploration of Dynamical System Analysis
The study employed dynamical system analysis to explore the phase space of the models and evaluate their stability. Future research could further investigate the use of dynamical system analysis as a means to validate and comprehend the cosmological implications of $f(Q)$ theories.
5. Comparison with the $Lambda$CDM Model
The study affirms the potential of higher-curvature gravity with boundary terms as a promising alternative to the $Lambda$CDM concordance model. Future research should continue to compare and contrast these two models to better understand their similarities, differences, and implications for our understanding of the universe.
Potential Challenges and Opportunities
- Challenges: One potential challenge in future research is the complexity of the mathematical models and equations involved in studying higher-curvature gravity with boundary terms. Researchers will need to develop sophisticated mathematical and computational techniques to overcome these challenges.
- Opportunities: The study highlights the potential of higher-curvature gravity with boundary terms as an alternative framework for understanding the universe. This opens up opportunities for interdisciplinary collaborations between cosmologists, mathematicians, and physicists to further explore and develop these theories.
Conclusion
The study demonstrates the efficacy of $f(Q)$ theories, grounded on non-metricity, in portraying late-time universe phenomena. It establishes constraints on two prevalent models within this framework and highlights the potential of higher-curvature gravity with boundary terms as a promising alternative to the $Lambda$CDM concordance model. Future research should continue to explore these theories, investigate alternative models, refine constraints, and compare with the $Lambda$CDM model. Challenges in complexity can be overcome through interdisciplinary collaborations, presenting exciting opportunities for further advancements in our understanding of the cosmos.
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