Inflation scenario in a non-minimal f(Q) gravity model

In the context of $f\left(Q\right)$ gravity, cosmological inflation takes a different turn. $f\left(Q\right)$ gravity is a modified theory of gravity, where the Lagrangian is a function of the non-metricity scalar Q. $f\left(Q\right)$ gravity theory is part of an extensive class of modified gravity theories designed to explain the accelerated expansion of the universe without the requirement for dark energy. In this paper, we study the modified gravity $f\left(Q\right)$ in which the scalar field is non-minimally coupled with the matter (it has a new interaction term $\alpha Q(1+{\varphi }^2)$ with the inflaton scalar field (ϕ) and non-metricity scalar (Q)). In pursuit, an inflationary model is extended and investigated by determining the slow-roll parameters and obtaining the model's linear perturbations after calculating the field equation. By comparing the model parameters with the CMB observational data, the model is adapted to observational data through the constraint of the parameters. After some numerical calculations, we show our model is consistent with observational data and free of the phantom if $1<\alpha <1.5$ and $1.42<{\gamma }_2<1.75$.