Cosmic perturbations with running G and Λ

Abstract with running cosmological term ? ? and gravitational Newton's coupling G may naturally be expected if the evolution of the universe can ultimately be derived from the first principles of Quantum Field Theory or String Theory. For example, if matter is conserved and the vacuum energy density varies quadratically with the expansion rate as ? ? (H) = n 0 + n 2 H 2, with n 0 ? = 0 (a possibility that has been advocated in the literature within the QFT framework), it can be shown that G must vary logarithmically (hence very slowly) with H. In this paper, we derive the general cosmological perturbation equations for models with variable G and ? ? in which the fluctuations ?G and ?? ? are explicitly included. We demonstrate that, if matter is covariantly conserved, the late growth of matter density perturbations is independent of the wavenumber k. Furthermore, if ? ? is negligible at high redshifts and G varies slowly, we find that these cosmologies produce a matter power spectrum with the same shape as that of the ?CDM model, thus predicting the same basic features on structure formation. Despite this shape indistinguishability, the free parameters of the variable G and ? ? models can still be effectively constrained from the observational bounds on the spectrum amplitude.