Cosmological scenarios in f ( Q , C ) gravity with a dynamical degree of freedom

Abstract The f ( Q , C ) theory, which extends symmetric teleparallel gravity by including the boundary term C in addition to the non-metricity scalar Q , provides a unifying framework that encompasses both f ( Q ) and f ( R ˚ ) gravities. In this work, we develop a comprehensive dynamical system analysis of f ( Q , C ) cosmology formulated within the non-coincident affine connection branches. Unlike the coincident case, these branches introduce a dynamical degree of freedom that significantly enriches the cosmological phase space. We show that even for simple power-law forms of the Lagrangian, the theory accommodates a broad spectrum of cosmic scenarios, including successive pressureless matter eras, stiff-matter phases between early inflation and dark matter domination, and late-time acceleration. Our analysis demonstrates that the Universe can naturally evolve from an initial de Sitter (dS) phase to a matter-dominated epoch and subsequently to a final dS attractor, consistent with the observed thermal history. These results highlight the role of the dynamical connection in shaping cosmic evolution and underline the potential of f ( Q , C ) gravity as a viable alternative framework for addressing outstanding issues in modern cosmology.