The classical stability of the ghost condensate

We discuss the classical stability of the cosmological mechanism which is responsible for the ghost condensation. We show that the simplest general covariant effective action which includes two covariant derivatives may lead to an overshoot of the condensation point into the regime where the model becomes classically unstable. The model exhibits this behaviour for the de Sitter and matter/radiation dominated Universes even when the initial values are taken to be in the region of validity of the low-energy effective theory. In the matter/radiation dominated case there is a finite time ( which can be large enough to exceed the present age of the Universe) during which the model remains in the stable region. In an inflationary regime the system does not experience an overshoot only if H-inf greater than or similar to M, where H-inf is the Hubble parameter during inflation, and M is the characteristic scale of the effective field theory (EFT). This latter regime is, however, inconsistent with the EFT description at the condensation point. We discuss the limitations of the use of the truncated action and point out how one can avoid problems due to the overshoot in order to have a viable ghost condensation mechanism.