An accelerating universe and cosmological perturbation in the ghost condensate

In the simplest Higgs phase of gravity called ghost condensation, an accelerating universe with a phantom era (w < -1) can be realized without ghosts or any other instabilities. In this paper we show how to reconstruct the potential in the Higgs sector Lagrangian from a given cosmological history (H(t), rho(t)). This in principle allows us to constrain the potential via geometrical information on the universe such as the supernova distance - redshift relation. We also derive the evolution equation for cosmological perturbations in the Higgs phase of gravity by employing a systematic low energy expansion. This formalism is expected to be useful for testing the theory with dynamical information on the large scale structure in the universe such as the cosmic microwave background anisotropy, weak gravitational lensing and galaxy clustering.