Gauge-invariant cosmological perturbation theory with seeds

Gauge-invariant cosmological perturbation theory is extended to handle perturbations induced by seeds. A calculation of the Sachs-Wolfe effect is presented. A second-order differential equation for the growth of density perturbations is derived and the perturbation of Liouville's equation for collisionless particles is also given. The results are illustrated by a simple analytic example of a single texture knot, where we calculate the induced perturbations of the energy of microwave photons, of baryonic matter, and of collisionless particles