Singularity Free Star Model Characterized by Quintessence Field in Quadratic f ( Q ) $f(Q)$ Gravity

In the context of the $f\left(Q\right)$ theory of gravity, a spherically symmetric quintessence DE model in this article is offered. For this reason, $f\left(Q\right)$ has the formula $f\left(Q\right)=a{Q}^2+Q$, where Q stands for the non-metricity scalar and ‘a’ is the coupling constant for modified gravity has been taken into account. It is supposed that the quintessence field defined by the parameter ${\omega }_q$, where ${\omega }_q\in (-1,-\frac{1}{3})$, controls the energy-momentum tensor of the underlying fluid distribution. The relationship between several physical parameters for the selected values of ‘a’, by choosing the metric potentials suggested by the Krori-Barua [Krori and Barua; J. Phys. A, Math. Gen. 8: 508, 1975] is investigated. Further, a number of analyses in detail to examine the physical validity of the proposed stellar model are carried out. The consequences of the compact star system caused by the connection of matter and geometry are succinctly described. The maximum allowable mass and radius for our present model for different values of ‘a’ have been studied by $M-R$ and $M-{\rho }_c$ curve. One can recover the usual general relativity (GR) standard results for $a=0$.