The evolutionary behavior of the Universe has been analysed through the
dynamical system analysis in $f(T,B,T_G,B_G)$ gravity, where $T$, $B$, $T_G$,
and $B_G$ respectively represent torsion, boundary term, teleparallel
Gauss-Bonnet term and Gauss-Bonnet boundary term. We use the transformation,
$f(T,B,T_G,B_G)=-T+mathcal{F}(T, B, T_G, B_G)$ in order to obtain the
deviation from the Teleparallel Equivalent of General Relativity (TEGR). Two
cosmological models pertaining to the functional form of $mathcal{F}(T, B,
T_G, B_G)$ have been studied. The well motivated forms are: (i) $mathcal{F}(T,
B, T_G, B_G) = f_{0} T^{m} B^{n}T_{G}^{k}$ and (ii) $mathcal{F}(T, B, T_G,
B_G)=b_{0} B + g_{0} T_{G}^{k} $. The evolutionary phases of the Universe have
been identified through the detailed analysis of the critical points. Further,
with the eigenvalues and phase space diagrams, the stability and attractor
nature of the accelerating solution have been explored. The evolution plots
have been analyzed for the corresponding cosmology and compatibility with the
present observed value of standard density parameters have been shown.
The article examines the evolutionary behavior of the Universe using dynamical system analysis in $f(T,B,T_G,B_G)$ gravity. It introduces the transformation $f(T,B,T_G,B_G)=-T+mathcal{F}(T, B, T_G, B_G)$ to study the deviation from the Teleparallel Equivalent of General Relativity (TEGR). Two cosmological models based on the functional form of $mathcal{F}(T, B, T_G, B_G)$ are analyzed:
- $mathcal{F}(T, B, T_G, B_G) = f_{0} T^{m} B^{n}T_{G}^{k}$
- $mathcal{F}(T, B, T_G, B_G)=b_{0} B + g_{0} T_{G}^{k}$
The critical points are identified and analyzed to understand the evolutionary phases of the Universe. The stability and attractor nature of the accelerating solution are explored using eigenvalues and phase space diagrams. Evolution plots are examined to determine compatibility with the present observed value of standard density parameters.
Future Roadmap:
In the future, further analysis and research can be conducted to build upon the conclusions of this study. Potential challenges and opportunities on the horizon include:
- Exploring Alternative Functional Forms: While two functional forms have been studied in this analysis, there may be other mathematical expressions that can better describe the evolutionary behavior of the Universe within $f(T,B,T_G,B_G)$ gravity. Further exploration of different forms can provide a more comprehensive understanding.
- Investigating Additional Cosmological Models: In addition to the two cosmological models studied in this analysis, there may be other models that can better capture the behavior of the Universe. Examining different cosmological models can provide insights into alternative scenarios and help validate or refine the conclusions drawn from this study.
- Refining Stability Analysis: While stability and attractor nature have been explored using eigenvalues and phase space diagrams, further analysis can be done to improve the accuracy and consistency of these results. Refining the stability analysis can provide a more robust understanding of the long-term behavior of the Universe.
- Validating with Experimental Data: While compatibility with the present observed value of standard density parameters has been shown, future research should focus on validating the conclusions of this analysis with experimental data from observations and experiments. This can help ensure the reliability and applicability of the findings in real-world scenarios.
- Implications for Cosmology and Physics: The conclusions derived from this study have important implications for our understanding of cosmology and physics. Exploring these implications and their potential applications can lead to advancements in various fields, such as astrophysics, cosmology, and quantum gravity.
By addressing these challenges and exploring these opportunities, researchers can further enhance our understanding of the evolutionary behavior of the Universe within $f(T,B,T_G,B_G)$ gravity, leading to new insights and potential breakthroughs in the field of theoretical physics.