A Geometric Framework for Cosmic Acceleration

We investigate a cosmological extension of the curvature-field framework in which cosmic acceleration is associated with the temporal evolution of a geometric deformation field rather than with an explicitly introduced cosmological-constant term. A deformation--transport principle and a minimal temporal closure are introduced to construct the homogeneous cosmological background. The resulting expansion history is first constrained using DESI DR2 baryon acoustic oscillation measurements and is then tested, with the DESI-determined parameter held fixed, against the Pantheon+ Type-Ia supernova sample. The CFF expansion history is not rejected by the independent Pantheon+ test, although flat $\Lambda$CDM provides a modestly lower chi-square for both datasets. A joint DESI--Pantheon+ analysis gives a parameter value consistent with the DESI-only determination. These results show that the curvature-field framework provides a viable and testable geometric description of the homogeneous cosmic expansion without an explicit cosmological-constant term. Cosmic acceleration can be described in the curvature-field framework as an effect of evolving geometric degrees of freedom.