Geometric acceleration in f(Q, C) theories

The f ( Q, C ) framework of gravity enables the depiction of an effective dark energy fluid that emerges from geometry itself, thus leading to modifications in the cosmological phenomenology of General Relativity. We pursue this approach to discover new and observationally supported (effective) evolving dark energy models. We propose a general f ( Q, C ) formulation that cannot be simply split into separate functions of Q and C , yet it still results in second-order field equations. By employing a particular type of connection, we derive guidelines for new cosmological models, including a variant of the DGP model that appears to be statistically favored over ΛCDM. Notably, we also demonstrate how to translate solutions within this f ( Q, C ) framework to f ( Q ) counterparts at the background level.