Cosmological Perturbations in Renormalization Group Derived Cosmologies

A linear cosmological perturbation theory of an almost homogeneous and isotropic perfect fluid Universe with dynamically evolving Newton constant $G$ and cosmological constant $\mathrm{\Lambda }$ 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 $\mathrm{\Lambda }$ are thus obtained. Explicit solutions are discussed in cosmologies where both $G$ and $\mathrm{\Lambda }$ vary according to renormalization group equations in the vicinity of a fixed point.