Quintessence like behavior of symmetric teleparallel dark energy: Linear and nonlinear model

In Einstein's General Relativity (GR), the gravitational interactions are described by the spacetime curvature. Recently, other alternative geometric formulations and representations of GR have emerged in which the gravitational interactions are described by the so-called torsion or non-metricity. Here, we consider the recently proposed modified symmetric teleparallel theory of gravity or $f\left( Q\right)$ gravity, where $Q$ represents the non-metricity scalar. In this paper, motivated by several papers in the literature, we assume the power-law form of the function $$ as $f\left( Q\right) =\alpha Q^{n+1}+\beta$ (where $$, $\beta$, and $n$ are free model parameters) that contains two models: Linear ($n=0$) and nonlinear ($n\neq 0$). Further, to add constraints to the field equations we assume the deceleration parameter form as a divergence-free parametrization. Then, we discuss the behavior of various cosmographic and cosmological parameters such as the jerk, snap, lerk, $Om$ diagnostic, cosmic energy density, isotropic pressure, and equation of state (EoS) parameter with a check of the violation of the strong energy condition (SEC) to obtain the acceleration phase of the Universe. Hence, we conclude that our cosmological $f(Q)$ models behave like quintessence dark energy (DE).