On the equation of state of dark energy

The formalism in order to obtain the dark energy equation of state is extended to non-flat universes and we consider the inequalities that must be satisfied by phantom dark energy in this case. We show that due to a non-vanishing spatial curvature satisfying the observational bounds, the uncertainty on the determination of the dark energy equation of state parameter w, when it is taken constant, can be significant and that it is minimal for some redshift zcr∼3. We consider the potential of future measurements of the gravitational waves emitted by binaries at high redshifts z>zcr to reduce this uncertainty. Results obtained here should also be relevant for a weakly varying equation of state with w≈−1.