Dynamical System Analysis of Scalar Field Cosmology in \(\boldsymbol{f(Q,T)}\) Gravity with \(\boldsymbol{q(z)}\) Parametrization

We explore the cosmological characteristics of the function of \(f(Q,T)=\alpha Q+\beta\sqrt{Q}+\gamma T\) where \(\alpha\), \(\beta\) and \(\gamma\) are constants. This investigation is conducted by considering the deceleration parameter in the form \(q(z)=q_{0}+q_{1}\dfrac{z(1+z)}{1+z^{2}}\), where \(q_{0}\) and \(q_{1}\) are constants. We apply combined Hubble \(46\) and BAO \(15\) data sets to determine the present value of the cosmological parameters. At the \(1-\sigma\) and \(2-\sigma\) confidence levels, we obtain the value of \(q_{0}=-0.373^{+0.072}_{-0.070}\). Additionally, the plot of \(q\) vs. \(z\) shows the accelerated stage of the Universe. We compute \(H(z)\) using the given form of \(q(z)\). We examine the behavior of all physical parameters using the expression for \(H(z)\). We also analyze the statefinder pairs \({r,s}\) and plot the \(r-s\) and \(r{-}q\) planes. They describe the \(\Lambda\)CDM period for our model. Once more, we investigate the \(Om(z)\) parameter and the sound speed in this study. The Universe is in a phantom epoch and remains stable. We also employ dynamical systems in our model, considering two distinct forms of the scalar potential. We identify the equilibrium points for both models. For Model 1, three stable equilibrium points are identified, while for Model 2, two stable points are determined. The phase diagram elucidates stability criteria of the equilibrium points. We explore the parameters \(\Omega_{\phi}\), \(q\), \(\omega_{\phi}\) and \(\omega_{\textrm{eff}}\) at each equilibrium point. The characteristic values of both models are investigated. Based on all calculations, we conclude that our model is stable and consistent with all observational data indicating that the Universe is in a phase of accelerated expansion.