Title: Exploring Weak measurements within the Einstein-Dirac Cosmological framework

Abstract: Our study applies the Two-State Formalism alongside weak measurements within a spatially homogeneous and isotropic cosmological framework, wherein Dirac spinors are intricately coupled to classical gravity. To elucidate this, we provide detailed formulations for computing the weak values of the energy-momentum tensors, the Z component of spin, and the characterization of pure states. Weak measurements appear to be a generalization and extension of the computation already made by Finster an Hainzl, in A spatially homogeneous and isotropic Einstein-Dirac cosmology. Our analysis reveals that the acceleration of the Universe expansion can be understood as an outcome of postselection, underscoring the effectiveness of weak measurement as a discerning approach for gauging cosmic acceleration.