The cosmological significance of boundary term in non-metricity gravity

Within the context of metric-affine gravity, we examine the significance of the boundary term in symmetric teleparallel gravity by employing the cosmological dynamical system analysis method. We focus on the novel gravity models characterized by the functions $f(Q,C)$, where f is a smooth function of the non-metricity scalar Q and the associated boundary term C. In a cosmological setting adopting three different classes of symmetric teleparallel affine connections, we investigate a model $f(Q,C)=Q^s+e{C}^r$, and some special cases of this model. We show that the boundary term which is added to the Einsteinian field equations (or equivalently to $f\left(Q\right)=Q$ ones) is capable of bringing forward solutions corresponding to the early accelerated expansion. This alludes the physics behind the boundary terms which usually are discarded in the most gravitational theories.