A theoretical framework is developed to calculate linear perturbations in the gravitational and matter fields which arise causally in response to the presence of stiff matter sources in a FRW cosmology. It is shown that, in order to satisfy energy and momentum conservation, the gravitational fields of the source must be compensated by perturbations in the matter and gravitational fields, and the role of such compensation in containing the initial inhomogeneities in their subsequent evolution is discussed. A complete formal solution is derived in terms of Green functions for the perturbations produced by an arbitrary source in a flat universe containing cold dark matter. Approximate Green function solutions are derived for the late-time density perturbations and late-time gravitational waves in a universe containing a radiation fluid. A cosmological energy-momentum pseudotensor is defined to clarify the nature of energy and momentum conservation in the expanding universe.