Phase-space analysis of a novel cosmological model in $f(Q)$ theory

The vanishing affine connections have been used solely while adopting the modified $f(Q)$ gravity theory to the cosmology. Consequently, researchers could not get beyond what is already known in $f(T)$ theory earlier. To alleviate this problem, in the present manuscript we investigate a recently proposed construction of $f(Q)$ theory using non-vanishing affine connection in the spatially flat FLRW spacetime. We then investigate the cosmological solutions of $f(Q)$ theory for a perfect fluid through the phase space analysis. We introduce few variables and dimensionless parameters to construct the corresponding equations suitable for the dynamical system approach. The conservation of the energy-momentum tensor leads to a constraint equation that relates the dynamical variables. Briefly, both unstable and stable de Sitter solutions appear which correspond to early and late times accelerated expansions. Also, unstable points corresponding to the matter dominated and radiation dominated eras have been found which do exist for every $f(Q)$ function. As a result, the present discussion shows that $f(Q)$ gravity endowed by non-vanishing affine connections is capable of explaining a true sequence of cosmic eras.