Statefinder diagnostic and dynamical stability of some f(Q) gravity models

This paper explores the possibility of producing the late-time cosmic acceleration in f(Q) gravity via some recently proposed gravity models namely the power-law model: f(Q)=Q+alpha Q2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(Q)=Q+\alpha Q<^>{2}$$\end{document}, and the exponential model: f(Q)=Qe lambda Q0Q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(Q)=Qe<^>{\frac{\lambda Q_{0}}{Q}}$$\end{document}, where Q is the non-metricity scalar. To achieve this target, a homogenous and isotropic space-time model with perfect fluid distribution involving radiation is taken into account. We study the dynamical behavior of both models by exploring some worthy cosmological parameters graphically including the equation of state parameter (omega)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\omega )$$\end{document}, the deceleration parameter (q), the squared speed of sound (vs2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(v<^>2_s)$$\end{document}, the jerk and snap pair (j, s) as well as Om(z)-diagnostic. The evolutionary trajectories in the j-s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$j-s$$\end{document} plane show different evolutionary characteristics favoring the expanding nature of universe. It is found that the square sound speed parameter vs2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v<^>2_s$$\end{document} can yield the stability of models under specific set of model parameters. Further, in order to define the cosmological behavior and stability of both models, we apply the dynamical system analysis to get the possible critical points for each model. We discuss the stability corresponding to each critical point through two-dimensional phase portrait. For both models, it is observed that there exists at least one stable node. Also, we explore the evolutionary behavior of density parameters for these models, which is associated with different phases of the universe. It is concluded that the proposed f(Q) models can lead to late-time cosmic evolution successfully in some subspaces of the model parameter's space.