Can an Extra Degree of Freedom in Scalar-Tensor Non-Metricity Gravity Account for the Evolution of the Universe?

Abstract: We investigate whether the extra scalar degree of freedom that arises in the second connection class of scalar-tensor non-metricity gravity can accurately replicate and potentially enrich the cosmic expansion history. Focusing on a spatially flat FLRW background, we introduce Hubble-normalized variables and recast the field equations into an autonomous dynamical system. Four representative scenarios are analyzed comprehensively. Phase-space research reveals a rich hierarchy of critical points: matter-dominated, stiff-fluid, and de Sitter solutions, together with asymptotic trajectories leading to Big-Crunch/Rip singularities and transient, unstable matter epochs. With suitable parameter choices, the standard $\Lambda$CDM sequence is reinstated; however, novel late-time and high-curvature regimes arise exclusively from the non-metricity sector. A systematic comparison of metric scalar-tensor and teleparallel scalar-torsion theories reveals unique stability characteristics and potential observational discriminants. Our findings indicate that the additional time-dependent function inherent to scalar-tensor non-metricity gravity can effectively explain the Universe's evolution while providing new phenomenology that can be tested by upcoming surveys.