Noncovariance of the dressed-metric approach in loop quantum cosmology

The dressed-metric approach is shown to violate general covariance by demonstrating that it cannot have an off-shell completion in which the correct infinitesimal relations of space-time hypersurface deformations are realized. The main underlying reason - a separation of background degrees of freedom and modes of inhomogeneity that is incompatible with covariance - is shared with other approaches such as hybrid loop quantum cosmology.