A Unified Dark Sector Framework: Sterile Neutrino Condensates and Dynamical Curvature Coupling for Late-Time Cosmic Acceleration

The standard cosmological paradigm (Lambda-CDM) requires two disconnected, ad-hoc dark components: collisionless cold dark matter (27%) and a severely fine-tuned bare cosmological constant (68%). In this paper, we formulate a unified dark sector framework wherein a single Beyond-the-Standard-Model (BSM) scalar field simultaneously generates cold dark matter phenomenology on galactic scales and accelerated cosmic expansion at cosmological epochs. The action features an ultra-light scalar non-minimally coupled to the Ricci curvature scalar (1/2 xi phi^2 R) and Yukawa-coupled to right-handed sterile neutrinos. In the high-density galactic regime (H << m_phi), fast coherent oscillations of the field yield an effective pressureless equation of state (w_eff approx 0), forming stable solitonic cores that naturally eliminate the core-cusp anomaly. On cosmological scales (H ~ H_0), the non-minimal curvature coupling drives a dynamical phase-space attractor wherein the effective dark energy equation of state asymptotically approaches w -> -1. We prove that the cosmic coincidence problem (rho_DM ~ rho_DE today) is naturally resolved as the transition epoch is dynamically triggered when the expansion rate drops below the scalar mass threshold: H^2 ~ xi m_phi^2. The model eliminates the 10^120 vacuum energy fine-tuning and exhibits precise alignment with Planck 2018, Pantheon+, and DESI observational bounds.