We propose a novel cosmological framework within the $f(R,T)$ type modified gravity theory, incorporating a non-minimally coupled with the higher order of the Ricci scalar ($R$) as well as the trace of the energy-momentum tensor ($T$). Therefore, our well-motivated chosen $f(R,T)$ expression is $ R + R^m + 2 lambda T^n$, where $lambda$, $m$, and $n$ are arbitrary constants. Taking a constant jerk parameter ($j$), we derive expressions for the deceleration parameter ($q$) and the Hubble parameter ($H$) as functions of the redshift $z$. We constrained our model with the recent Observational Hubble Dataset (OHD), $Pantheon$, and $ Pantheon $ + OHD datasets by using the analysis of Markov Chain Monte Carlo (MCMC). Our model shows early deceleration followed by late-time acceleration, with the transition occurring in the redshift range $1.10 leq z_{tr} leq 1.15$. Our findings suggest that this higher-order model of $f(R,T)$ gravity theory can efficiently provide a dark energy model for addressing the current scenario of cosmic acceleration.
We propose a novel cosmological framework within the $f(R,T)$ type modified gravity theory. This framework incorporates a non-minimally coupled higher order of the Ricci scalar ($R$) as well as the trace of the energy-momentum tensor ($T$). Our chosen $f(R,T)$ expression is $ R + R^m + 2 lambda T^n$, where $lambda$, $m$, and $n$ are arbitrary constants.
By taking a constant jerk parameter ($j$), we have derived expressions for the deceleration parameter ($q$) and the Hubble parameter ($H$) as functions of the redshift $z$. We have constrained our model using the recent Observational Hubble Dataset (OHD), $Pantheon$, and $Pantheon + OHD$ datasets through the analysis of Markov Chain Monte Carlo (MCMC).
Our results show that our model exhibits early deceleration followed by late-time acceleration, with the transition occurring in the redshift range .10 leq z_{tr} leq 1.15$. This suggests that our higher-order model of $f(R,T)$ gravity theory can effectively provide a dark energy model to address the current scenario of cosmic acceleration.
Future Roadmap
Challenges
- Data Accuracy: One challenge that researchers may face is ensuring the accuracy and reliability of the observational data used to constrain and validate our proposed model. It is important to continue improving observational techniques and minimizing systematic errors in order to obtain more precise results.
- Theoretical Development: Further theoretical development and analysis may be required to fully understand and interpret the implications of our proposed framework within the $f(R,T)$ modified gravity theory. This includes exploring potential connections with other cosmological models and addressing any limitations or assumptions made in our current model.
Opportunities
- Further Testing: Our model can be further tested and validated using future observations and surveys, such as those planned by upcoming space missions or ground-based observatories. These additional data points can help refine and improve our understanding of the cosmological framework and its predictions.
- Extensions and Modifications: Researchers have the opportunity to extend and modify our proposed $f(R,T)$ gravity theory framework to explore alternative models and incorporate additional physical factors. This can help address other open questions in cosmology, such as the nature of dark matter or the existence of primordial gravitational waves.
In conclusion, our study presents a promising cosmological framework within the $f(R,T)$ modified gravity theory. The use of observational data and MCMC analysis supports the viability of our model in providing a dark energy explanation for the current cosmic acceleration scenario. However, further research, including improvements in data accuracy and theoretical development, is necessary to fully understand and explore the potential of this framework.