Phase space analysis of cosmological models on $f(R,G,T)$ gravity

In the present article, we developed a dynamical system in the context of modified $f(R,G,T)$ gravity, where $R$, $G$ and $T$ are Ricci scalar, Gauss-Bonnet term and energy-momentum tensor respectively. Development of the dynamical system is done by first defining 9 dimensionless variables and formulate a ordinary differential equations by taking derivative of the variables with respect to logarithmic time $N=\log a(t)$, where $a(t)$ is the scale factor. This formulation is applied to the model $f(R,G,T)=\alpha R^{l}+\beta G^{m} + \gamma T^{n}$, and its solutions and their corresponding stabilities are analysed in details. From the plot of density parameters vs $N=-log(1+z)$, we conclude that our Universe is currently dominated by dark energy, which is compatible with current observation. Taking $l=2$, cosmic parameters such as deceleration parameter $(q)$, equation of state $(\omega)$ and state finder parameters are also discussed by fixing one dimensionless variable, showing our Universe's expansion is accelerating with the present value of $q=-0.5$. Present value of $\omega=-0.66$ suggests that our Universe is in Quintessence phase. Lastly, the validity of the model with respect to the $\Lambda$CDM model is checked by using 77 Hubble, 15 BAO and 1024 pantheon datasets, which implies that our model is aligned with the $\Lambda$CDM model's bahaviour.