Cosmic Backgrounds in the Gravitational Standard-Model Extension

We consider background fields within the gravitational sector of the Standard-Model Extension (SME) in a cosmological setting. Our analysis is divided into two parts. The first part addresses the consistency of nondynamical backgrounds in scenarios where diffeomorphism invariance is explicitly broken. Focusing on gravitational systems that admit Killing vector fields and possess a priori symmetries, we demonstrate that potential discrepancies between Riemannian geometry and dynamical equations can be avoided. The second part presents a direct application of various techniques developed by decomposing the modified Einstein equations along normal and tangential directions of the (3+1) decomposition. We show that nondynamical backgrounds can lead to accelerated cosmological expansion without requiring a cosmological constant, thereby opening new avenues for interpreting dark energy.