A linear cosmological perturbation theory of an almost homogeneous and
isotropic perfect fluid Universe with dynamically evolving Newton constant G
and cosmological constant Λ 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 Λ are thus obtained. Explicit solutions
are discussed in cosmologies where both G and Λ vary according to
renormalization group equations in the vicinity of a fixed point.Comment: 22 pages, revtex, subeqn.sty, to appear on IJMP