Aether SUSY breaking: Can aether be alternative to F-term SUSY breaking?

We investigate supersymmetry (SUSY) breaking scenarios where both SUSY and Lorentz symmetry are broken spontaneously. For concreteness, we propose models in which scalar fluid or vector condensation breaks Lorentz symmetry and accordingly SUSY. Then, we examine whether such scenarios are viable for realistic model buildings. We find, however, that the scalar fluid model suffers from several issues. Then, we extend it to a vector condensation model, which avoids the issues in the scalar fluid case. We show that accelerated expansion and soft SUSY breaking in matter sector can be achieved. In our simple setup, the soft SUSY breaking is constrained to be less than $\mathcal{O}(100)$TeV from the constraints on modification of gravity.