  A linear cosmological perturbation theory of an almost homogeneous and
isotropic perfect fluid Universe with dynamically evolving Newton constant $G$
and cosmological constant $\Lambda$ is presented. A gauge-invariant formalism
is developed by means of the covariant approach, and the acoustic propagation
equations governing the evolution of the comoving fractional spatial gradients
of the matter density, $G$, and $\Lambda$ are thus obtained. Explicit solutions
are discussed in cosmologies where both $G$ and $\Lambda$ vary according to
renormalization group equations in the vicinity of a fixed point.
