Density perturbations for a running cosmological constant

Abstract

The dynamics of density and metric perturbations is investigated for the previouslydeveloped model where the decay of the vacuum energy into matter (or viceversa) is due to the renormalization group (RG) running of the cosmologicalconstant (CC) term. The evolution of the CC depends on the single parameterν, which characterizes the running of the CC produced by the quantum effects of matterfields of the unknown high energy theory below the Planck scale. The sign ofν indicates whether bosons or fermions dominate in the running. The spectrum of perturbationsis computed assuming an adiabatic regime and an isotropic stress tensor. Moreover, theperturbations of the CC term are generated from the simplest covariant form suggested bythe RG model under consideration. The corresponding numerical analysis shows that forν > 0 there isa depletion of the matter power spectrum at low scales (large wavenumbers) as compared to the standardΛCDM model,whereas for ν < 0 there is an excess of power at low scales. We find that the LSS data rule out the range|ν| > 10−4 while the values|ν| ≤ 10−6 look perfectlyacceptable. For ν < 0 the excess of power at low scales grows rapidly and the bound is more severe. From theparticle physics viewpoint, the values |ν| ≃ 10−6 correspond to the ‘desert’ in the mass spectrum above the GUT scaleMX ∼ 1016 GeV. Our results are consistent with those obtained in other dynamical models admitting aninteraction between dark matter and dark energy. We find that the matter power spectrumanalysis is a highly efficient method for discovering a possible scale dependence of thevacuum energy.