General relativity limit of Horava-Lifshitz gravity with a scalar field in gradient expansion

Understand

We present a fully nonlinear study of long wavelength cosmological perturbations within the framework of the projectable Horava-Lifshitz gravity, coupled to a single scalar field.

• Adopting the gradient expansion technique, we explicitly integrate the dynamical equations up to any order of the expansion, then restrict the integration constants by imposing the momentum constraint.
• While the gradient expansion relies on the long wavelength approximation, amplitudes of perturbations do not have to be small.
• When the $\lambda\to 1$ limit is taken, the obtained nonlinear solutions exhibit a continuous behavior at any order of the gradient expansion, recovering general relativity in the presence of a scalar field and the "dark matter as an integration constant".