Theories with limited extrinsic curvature and a nonsingular anisotropic
  universe
  We propose a class of theories that can limit scalars constructed from the
extrinsic curvature. Applied to cosmology, this framework allows us to control
not only the Hubble parameter but also anisotropies without the problem of
Ostrogradsky ghost, which is in sharp contrast to the case of limiting
spacetime curvature scalars. Our theory can be viewed as a generalization of
mimetic and cuscuton theories (thus clarifying their relation), which are known
to possess a structure that limits only the Hubble parameter on homogeneous and
isotropic backgrounds. As an application of our framework, we construct a model
where both anisotropies and the Hubble parameter are kept finite at any stage
in the evolution of the universe in the diagonal Bianchi type I setup. The
universe starts from a constant-anisotropy phase and recovers Einstein gravity
at low energies. We also show that the cosmological solution is stable against
a wide class of perturbation wavenumbers, though instabilities may remain for
arbitrary initial conditions.
