Noncoincidence f(Q)-Cosmology with Dark Matter Coupled to Gravity

Abstract

We investigate Friedmann–Lemaître–Robertson–Walker (FLRW) cosmology in the framework of symmetric teleparallel $f\left(Q\right)$ gravity with a nonminimal coupling between dark matter and the gravitational field. In the noncoincidence gauge, the field equations admit an equivalent multi-scalar field representation, which we investigate the phase-space using the Hubble-normalization approach. We classify all stationary points for arbitrary function $f\left(Q\right)$ and we discuss the physical properties of the asymptotic solutions. For the power-law theory, we perform a detailed stability analysis and show that the de Sitter solution is the unique future attractor, while the matter-dominated point appears as a saddle point. Moreover, there exist a family of scaling solutions that can be related to inflationary dynamics. In contrast with uncoupled $f\left(Q\right)$ models, the presence of the coupling introduces a viable matter-dominated era alongside late-time accelerated expansion. Our study shows that the coupling function plays a crucial role in cosmological dynamics in $f\left(Q\right)$ gravity.