A Manifestly Noncovariant Theory of Gravitation
  We study a noncovariant theory of gravitation based on the Lagrangian density $\sqrt{-g})^\omega R$, where $\omega$ is a constant. In particular, we study solutions that for $\omega=1$ reduces to the de Sitter, Kasner and LFRW (with perfect fluid with as a source). We also consider spherically symmetric solutions. 
Patricio.S. Letelier
gr-qc hep-th