Variation of parameters in cosmology

Parameters which appear in the solutions of the dynamical equations of spatially homogeneous cosmology or in the dynamical equations themselves are subject to algebraic relations imposed by the constraint equations, i.e., are confined to a constraint hypersurface in parameter space. Values of these parameters off the constraint hypersurface often correspond to solutions which have an additional stiff perfect fluid source that may or may not be flowing orthogonally to the spatially homogeneous foliation or to a related inhomogeneous but spatially self-similar solution or to a combination of the two. These possibilities are studied and explicitly illustrated, leading to a uniform derivation of most of the known exact anisotropic spatially homogeneous or spatially self-similar solutions as well as some new ones.