Observational constraints on a non-minimally coupled scalar field in non-metricity gravity with an extra degree of freedom

Abstract

We investigate a non-minimally coupled scalar field in non-metricity gravity, adopting a non-trivial connection class in spatially flat FLRW spacetimes. In contrast to the coincident-gauge choice, this connection class activates an additional dynamical degree of freedom (DoF) that modifies the background evolution. We study two representative models, defined by power-law and exponential coupling functions with the exponential potential for scalar field. Confronting both models with recent combined datasets - DESI BAO, two independent supernova compilations, and cosmic chronometers - we find that each reproduces an extended matter-dominated era followed by a stable late-time de-Sitter attractor, with inferred parameters consistent with the standard $Λ$CDM model. A complementary autonomous dynamical-system analysis identifies a sequence of critical points describing successive stiff-fluid, transient matter-dominated, and stable de-Sitter phases, ensuring a viable thermal history of the universe. The observational and dynamical results are mutually consistent and support the cosmological viability of the proposed models.