Spatially covariant theories of gravity: disformal transformation, cosmological perturbations and the Einstein frame

Understand

We investigate the cosmological background evolution and perturbations in a general class of spatially covariant theories of gravity, which propagates two tensor modes and one scalar mode.

• We show that the structure of the theory is preserved under the disformal transformation.
• We also evaluate the primordial spectra for both the gravitational waves and the curvature perturbation, which are invariant under the disformal transformation.
• Due to the existence of higher spatial derivatives, the quadratic Lagrangian for the tensor modes itself cannot be transformed to the form in the Einstein frame.